Akar-akar persamaan kuadrat bagian 2 : Melengkapi kuadrat sempurna

Summary

In this video, the host explains how to find the roots of quadratic equations using the method of completing the square. Through several examples, the steps for solving equations like x² + 6x + 8 = 0, 2x² + 7x + 3 = 0, and 3x² + 8x + 4 = 0 are demonstrated. Key concepts include factoring, manipulating fractions, and simplifying square roots. The tutorial aims to help viewers understand the process of solving quadratic equations step by step, ensuring clarity and ease of understanding for both beginners and those revisiting the topic.

Takeaways

• 😀 Understanding how to solve quadratic equations using the method of completing the square.
• 😀 The first example demonstrates how to solve the equation x² + 6x + 8 = 0 by completing the square.
• 😀 Completing the square involves moving constant terms to the other side and adding the square of half the middle term to both sides.
• 😀 Factoring the equation into (x + 3)² = 1 leads to solutions of x = -2 and x = -4.
• 😀 In the second example, the coefficient of x² is 2, requiring division of all terms by 2 before completing the square.
• 😀 Dividing all terms of the quadratic by 2 results in a simpler equation, x² + 7/2x + 3/2 = 0.
• 😀 After adding and subtracting (7/4)² to complete the square, the equation is factored into (x + 7/4)² = 25/16.
• 😀 Solutions are obtained by taking the square root of both sides, leading to values x = -1/2 and x = -3.
• 😀 The third example begins by dividing all terms by 3 to simplify the equation, turning 3x² + 8x + 4 = 0 into x² + 8/3x + 4/3 = 0.
• 😀 Completing the square in this case involves adding (8/6)² to both sides and factoring to obtain the equation (x + 4/6)² = 16/36.
• 😀 The final solution for the third example gives values of x = -2/3 and x = -2, emphasizing the importance of simplifying fractions during the process.

Q & A

What is the main topic of the video?

The main topic of the video is solving quadratic equations using the method of completing the square.

What is the first step in solving a quadratic equation by completing the square?

The first step is to rewrite the equation in the form 'x^2 + bx = c' by moving the constant term to the right side.

How do you determine the number to complete the square in the equation?

To complete the square, you take half of the coefficient of 'x', square it, and add it to both sides of the equation.

In the first example, how was the term to complete the square calculated?

In the first example, the coefficient of 'x' was 6. Dividing 6 by 2 gives 3, and squaring it gives 9. This number was added to both sides of the equation.

What is the final solution for the quadratic equation in the first example?

The final solutions for the quadratic equation x^2 + 6x + 8 = 0 are x = -2 and x = -4.

How is the equation adjusted when the leading coefficient is not 1?

When the leading coefficient is not 1, you divide the entire equation by the coefficient of x^2 to make the coefficient of x^2 equal to 1.

In the second example, how do you handle the coefficient of 2 in front of x^2?

In the second example, the equation 2x^2 + 7x + 3 = 0 is divided by 2 to make the leading coefficient 1, resulting in x^2 + (7/2)x + (3/2) = 0.

What happens when the denominator in the fractions becomes different in the second example?

When the denominators in the fractions differ, you find the least common denominator (LCD) and adjust the fractions accordingly before proceeding with the solution.

What does the factorized form of the quadratic equation look like in the second example?

The factorized form of the quadratic equation in the second example is (x + 7/4)^2 = 25/16.

What is the final solution for the quadratic equation in the second example?

The final solutions for the quadratic equation 2x^2 + 7x + 3 = 0 are x = -1/2 and x = -3/2.