omplete the square to solve the following quadratic equation: x2−6x−20=20%0D%0A%0D%0A2%0D%0A−%0D%0A6%0D%0A%0D%0A−%0D%0A20%0D%0A=%0D%0A20%0D%0A .(1 point)

Answer 1

To complete the square for the quadratic equation x^2 - 6x - 20 = 20, we need to add and subtract the square of half the coefficient of x.

First, let's move the constant term to the right side of the equation:

x^2 - 6x = 20 + 20

x^2 - 6x = 40

Next, take half of the coefficient of x, which is -6, and square it:

(-6/2)^2 = (-3)^2 = 9

Now, add and subtract 9 to the left side of the equation:

x^2 - 6x + 9 - 9 = 40

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

(x - 3)^2 - 9 = 40

Now, we can simplify the equation:

(x - 3)^2 = 40 + 9

(x - 3)^2 = 49

Taking the square root of both sides:

x - 3 = ±√49

x - 3 = ±7

Now, solving for x:

x = 3 + 7 = 10

x = 3 - 7 = -4

Therefore, the solutions to the quadratic equation x^2 - 6x - 20 = 20 are x = 10 and x = -4.