Question

Complete the square to solve the following quadratic equation: x2−6x−20=20 .(1 point) Responses x=10 , x=−4 x equals 10 , x equals negative 4 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=−10 , x=4 x equals negative 10 , x equals 4 x=52 , x=−46

Answer 1

To complete the square, we need to move the constant term to the right side of the equation:

x^2 - 6x - 20 = 20

Subtracting 20 from both sides:

x^2 - 6x - 40 = 0

To complete the square, we take half of the coefficient of x (-6), square it, and add it to both sides:

x^2 - 6x + (-6/2)^2 = 40 + (-6/2)^2
x^2 - 6x + 9 = 40 + 9

Simplifying:

x^2 - 6x + 9 = 49

Now, we can rewrite the left side as a perfect square:

(x - 3)^2 = 49

Taking the square root of both sides:

x - 3 = ±√49

x - 3 = ±7

Solving for x:

x = 3 + 7 = 10
x = 3 - 7 = -4

Therefore, the solutions are x = 10 and x = -4.