Complete the square to solve the following quadratic equation: x2−6x−20=20

Question

.(1 point)
Responses

x=3+210−−√, 3−210−−√
x equals 3 plus 2 Start Root 10 End Root comma 3 minus 2 Start Root 10 End Root

x=52
, x=−46
x equals 52 , x equals negative 46

x=−10
, x=4
x equals negative 10 , x equals 4

x=10
, x=−4

Answer 1

To solve the quadratic equation \( x^2 - 6x - 20 = 20 \) by completing the square, follow these steps:

1. Move the constant to the right side: \[ x^2 - 6x - 20 - 20 = 0 \ x^2 - 6x - 40 = 0 \ x^2 - 6x = 40 \]

2. Complete the square: Take half of the coefficient of \( x \) (which is -6), square it, and add it to both sides: \[ \left(-\frac{6}{2}\right)^2 = 9 \] So we add 9 to both sides: \[ x^2 - 6x + 9 = 40 + 9 \ x^2 - 6x + 9 = 49 \]

3. Rewrite the left side as a squared term: \[ (x - 3)^2 = 49 \]

4. Take the square root of both sides: \[ x - 3 = \pm 7 \]

5. Solve for \( x \): \[ x - 3 = 7 \implies x = 10 \ x - 3 = -7 \implies x = -4 \]

Thus, the solutions are: \[ x = 10, \quad x = -4 \]

So the correct answer is: x=10, x=−4