How to Solve These Quadratic Equations?
Summary
TLDRIn this educational video, the instructor demonstrates how to solve quadratic equations using the method of extracting square roots. They provide a step-by-step approach to simplifying equations and isolating the variable, offering two solutions for each example. The video is aimed at grade 10 students, with the instructor, Ram Islam, engaging viewers with clear explanations and practical examples. New subscribers are encouraged to like and subscribe for more educational content.
Takeaways
- 📚 The video is an educational tutorial focused on solving quadratic equations.
- 🔍 The first example involves simplifying the equation by eliminating constants and coefficients.
- 📉 The method of transposing terms to one side of the equation is demonstrated to isolate the variable.
- 🔢 The process of dividing both sides by a coefficient to simplify the equation is explained.
- 🆚 The use of square roots to solve for the variable is introduced, including both positive and negative roots.
- 📝 The importance of considering both the positive and negative square roots when solving is emphasized.
- ✂️ The concept of canceling out terms in the equation to simplify it further is shown.
- 📉 The second example involves dealing with fractional forms and demonstrates how to eliminate the fraction.
- 🔄 The tutorial covers multiplying both sides of the equation by the denominator to clear the fraction.
- 📌 The final step in both examples is to isolate the variable and solve for its possible values.
- 👨🏫 The presenter, MIDI turgon Ram Islam, encourages viewers to like and subscribe for more educational content.
Q & A
What is the main topic of the video?
-The main topic of the video is how to solve quadratic equations.
What method is suggested for solving the first quadratic equation in the video?
-The method suggested for solving the first quadratic equation is by extracting square roots.
How does the video suggest to handle the negative 42 in the first equation?
-The video suggests transposing the negative 42 to the other side of the equation to make it positive 42.
What is the next step after transposing the negative 42 in the first equation?
-The next step is to eliminate the positive six by dividing both sides of the equation by six.
What does the video suggest to do after simplifying the equation to 'five plus X squared equals seven'?
-The video suggests multiplying both sides of the equation by the conjugate to extract the square roots.
How does the video handle the extraction of square roots when 7 is not a perfect square?
-The video suggests taking the positive and negative square root of 7 and then isolating X by transposing 5 to the other side of the equation.
What are the two possible values of x for the first equation according to the video?
-The two possible values of x are (positive square root of 7) - 5 and (negative square root of 7) - 5.
What is the approach for solving the second equation in the video?
-The approach for the second equation is to first transpose negative 13 to the other side, then multiply both sides by the denominator to eliminate it, and finally extract the square roots.
How does the video suggest to simplify the equation after multiplying by the denominator in the second problem?
-The video suggests simplifying to '2x plus 3 squared equals 39' and then extracting the square roots to solve for x.
What are the two possible values of x for the second equation according to the video?
-The two possible values of x are (positive square root of 39 - 3) / 2 and (negative square root of 39 - 3) / 2.
Who is the presenter of the video and what is their closing remark?
-The presenter of the video is MIDI turgon, Ram Islam, and their closing remark is a reminder to like and subscribe for updates.
Outlines
📚 Solving Quadratic Equations by Square Roots
This paragraph introduces the process of solving quadratic equations using the square root method. The teacher begins by presenting the first problem, which involves an equation with a term 'six times the quantity of 5 plus X squared minus 42'. The initial step is to eliminate the negative term by transposing it to the other side of the equation, resulting in 'six times the quantity of five plus X squared equals 42'. The next step is to eliminate the coefficient of the quadratic term by dividing both sides by six, simplifying the equation to 'five plus X squared equals seven'. The teacher then demonstrates how to apply the square root method to solve for X, resulting in two potential solutions: 'X equals plus or minus the square root of seven minus five'. The paragraph concludes with a note on how to present the solutions in different forms if required by the teacher.
🔍 Step-by-Step Solution for Quadratic Equations
The second paragraph continues the theme of solving quadratic equations, focusing on a step-by-step approach for a specific problem. The equation '2X plus 3 squared equals negative 13' is presented, and the teacher explains how to transpose the negative term to the other side, resulting in '2X plus 3 squared equals 13'. The teacher then demonstrates the process of eliminating the denominator by multiplying both sides by three, leading to '2X plus 3 squared equals 39'. The square root method is applied next, yielding two potential solutions: 'X equals plus or minus the square root of 39 minus 3 divided by 2'. The teacher emphasizes the importance of considering these as the final answers and provides guidance on how to present alternative solutions if necessary. The paragraph ends with a reminder for viewers to subscribe to the channel for updates.
Mindmap
Keywords
💡Quadratic Equations
💡Extracting Square Roots
💡Transposing
💡Dividing by Coefficient
💡Perfect Square
💡Quadratic Terms
💡Radicand
💡Factoring
💡Fractional Forms
💡Solving for X
💡Properties of Equality
Highlights
Introduction to the topic of solving quadratic equations.
Explanation of different methods to solve quadratic equations.
Presentation of the first problem involving the equation 6(5 + x)^2 - 42.
Strategy to eliminate negative 42 by transposing it to the other side of the equation.
Simplification of the equation to resemble the form x^2 = k.
Division of both sides by 6 to isolate the quadratic term.
Use of the square root extraction method to solve the simplified equation.
Handling of the imperfect square by taking the positive and negative square roots.
Transposition of the constant term to isolate the variable.
Final simplification to find the two possible values of x.
Introduction of the second problem involving fractional forms.
Step-by-step guide on solving the second problem with fractional coefficients.
Multiplication of both sides by the denominator to eliminate the fraction.
Application of the square root extraction method to the new equation.
Isolation of the variable by transposing terms and dividing by the coefficient.
Presentation of the two possible solutions for x in the second problem.
Emphasis on the properties of equality in solving quadratic equations.
Conclusion summarizing the methods for solving quadratic equations in grade 10.
Encouragement for new subscribers to like and subscribe for updates.
Transcripts
hi guys it's me teacher gone in today's
video we will talk about how to solve
quadratic equations
so melaton different versions of this
kind of topic pero now
when it comes to solving quadratic
equations
so without further Ado let's do this
topic
so what we have here is the first
problem
we are given the equation
six times the quantity of 5 plus X
raised to the second power
minus 42 and to give you an idea
what we're going to use here is solving
quadratic equations by extracting the
square roots
and to solve this problem first we will
eliminate negative 42
guys you can add 42 both sides of
decoration but to make it easier for us
it will just transpose negative 42 to
the other side of the equation
that would make it positive for two so
what will happen our new equation is
six
times the quantity of five
plus X
squared
is equal to from negative it will become
just 42. then after that
guys is to follow this pattern we need
to make it
looks like a x squared
is equal to K that but
quadratic terms left side and then
constant on the other side so what's
next here is that we need to eliminate
positive six
so to eliminate that is
divide both sides
by six in this case you can cancel out
six
we can cancel out six
what we mean here is five
plus X
raised to the second power
is equal to 42 divided by 6 is
equal to
seven now
in your case maybe you will you would
think that we need to expand this one we
will try to
multiply 5 plus x times five plus X
perilous of using extracting the square
roots
connecting square roots now both sides
of the equation
credits and this one don't forget the
positive and negative and by the way
comment section
your radical and the Power of Two
invisible index not to
nah you may property if the index
and exponent of the radicand are equal
we can simply cancel it out
so what we have here is five
plus X
is equal to since 7 is not a perfect
square and well anti-factors
the seven
it only mean as positive negative
square root of seven
what's next is
five
by transposing it to the other side of
the equation so what we have now is
simply copier X
is equal to positive negative
squared off
seven then it will become minus 5. hang
on
um you can consider this one as an
answer key
this is simplified by you negative seven
so minus five okay acceptable in the end
but if your teacher or Professor asks
you for little different solutions you
can separate the two solutions
your first solution use the positive 7
square root of seven
that is square root of seven and then
copy
negative five so this is the first value
of x
now for the second solution which is the
x sub 2
we are done with the positive negative
you have negative square root of
seven
minus five foreign
if your teacher wants to factor the
negative sign
again negative times square root of
seven
plus five this one is possible so these
are the possible values of x
so Mejo
um
the properties of equality now let's
continue with item number two
in number two fractional forms are
better don't worry about it
I will teach you step by step on how to
solve this one
same thing that we learn to go in okay
x squared
is equal to K
right now
so left side
negative 13.
is equivalent to x squared okay
we will transpose negative 13 to the
other side of the equation
this will become
2X
plus 3
raised to the second power
over three transpose negative 13 to the
other side
it will become
positive 13. and here
in denominator three so what we need to
do is to eliminate it by
multiplying both sides of the equation
by this denominator
it will be canceled out is 2X
plus 3
raised to the second power and on the
other side 13 times 3 is
30
9.
so what's next
extract the square roots
x squared 39 is X is K
get a square root of this one and then
positive negative
cancel cancel
you have 2X
plus 3
is equal to
positive negative square root of 39.
okay
when is transpose this to the other side
of the equation
to become
2x is equal to positive negative square
root of
39
minus three
and lastly
and as a sold for X Style
divide both sides by two
cancel cancel
your
cash up your X move that internal
contact
your X
is equal to
positive negative square root of
39
minus 3 over
2. actually guys
you should consider this one as final
answer because a
uh factors
Solutions you can provide one
your x sub 1 here
square root of 39
minus 3 over
as the first value of x
for the second value of x
negative domain
negative square root of
39
minus 3 over 2 and these are the
possible values of x
so yo guys
on how to solve quadratic equations
on how to solve quadratic equations
for grade 10. so guys if you're new to
my channel
don't forget to like And subscribe
button
for you to be updated certain latest
uploads again it's MIDI turgon
Ram Islam
bye
تصفح المزيد من مقاطع الفيديو ذات الصلة
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