Ecuaciones cuadráticas de la forma ax2 + c=0

Summary

In this video, Prof. Robinson explains how to solve incomplete quadratic equations of the form x² + c = 0. He demonstrates two examples: one involving direct manipulation of the equation and the other using the difference of squares. In the first example, the equation -9x² + 3 = 0 is simplified to x² = 1/3, yielding two solutions. The second example, x² - 49 = 0, is solved by factoring as a difference of squares, resulting in x = ±7. Prof. Robinson emphasizes the importance of recognizing these forms to solve quadratic equations efficiently.

Takeaways

• 😀 Incomplete quadratic equations are of the form x² + c = 0, where the equation includes only the squared term and a constant, without a linear x term.
• 😀 When solving incomplete quadratic equations, the first step is to move the constant term to the other side of the equation.
• 😀 In the equation -9x² + 3 = 0, after moving the constant, we get -9x² = -3, then multiplying by -1 gives 9x² = 3.
• 😀 To isolate x², divide both sides of the equation by the coefficient of x². In the case of 9x² = 3, divide both sides by 9 to get x² = 1/3.
• 😀 To solve for x, take the square root of both sides. For x² = 1/3, x becomes ±√(1/3), or ±√3/3.
• 😀 In the second example, x² - 49 = 0 is recognized as a difference of squares, allowing us to factor the equation into (x + 7)(x - 7) = 0.
• 😀 After factoring a difference of squares, set each factor equal to zero: x + 7 = 0 and x - 7 = 0.
• 😀 Solving x + 7 = 0 gives x = -7, and solving x - 7 = 0 gives x = 7. These are the roots of the equation x² - 49 = 0.
• 😀 Recognizing a difference of squares in equations helps simplify the solving process by factoring them into two binomials.
• 😀 For equations of the form x² + c = 0, solving can involve either using the square root directly or factoring if a difference of squares is present.
• 😀 In summary, to solve incomplete quadratic equations, either take the square root of both sides or factor the equation if it's a difference of squares.

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