Complete the square to solve the following quadratic equation: x^2−6x−20=20 .(1 point) Responses x=−10 , x=4 x equals negative 10 , x equals 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=52 , x=−46 x equals 52 , x equals negative 46 x=10 , x=−4
To complete the square to solve the quadratic equation x^2 - 6x - 20 = 20, we begin by moving the constant term to the right side of the equation:
x^2 - 6x - 20 - 20 = 0
x^2 - 6x - 40 = 0
To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, half of -6 is -3, and when squared it becomes 9:
x^2 - 6x + 9 = 40 + 9
(x - 3)^2 = 49
Next, we take the square root of both sides to solve for x:
√(x - 3)^2 = ±√49
x - 3 = ±7
To solve for x, we add 3 to both sides:
x = 3 ± 7
This gives us two solutions:
x = 10 or x = -4.
So the correct response is:
x = 10, x = -4.