Complete the square to solve the following quadratic equation: x2−6x−20=20 .(1 point) Responses
x=−10 , x=4 x
x=−4
x=−46
46 x=3+210−−√, 3−210−−√
To solve the equation x^2 - 6x - 20 = 20, we can complete the square.
First, we move the constant term to the other side of the equation:
x^2 - 6x - 40 = 0
Next, we need to determine the value that completes the square. We take half of the coefficient of x and square it:
(-6/2)^2 = 9
To maintain the equality of the equation, we must also add 9 to both sides of the equation:
x^2 - 6x + 9 - 40 + 9 = 0
(x - 3)^2 - 40 = 0
Simplifying further:
(x - 3)^2 = 40
Taking the square root of both sides:
x - 3 = ±√40
x - 3 = ±2√10
Adding 3 to both sides:
x = 3 ± 2√10
Therefore, the solutions to the quadratic equation x^2 - 6x - 20 = 20 are:
x = 3 + 2√10
x = 3 - 2√10