Question

Complete the square to solve the following quadratic equation: x2−6x−20=20.(1 point)
Responses

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

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 10 , x equals negative 4

x=−10, x=4

Answer 1

To solve the quadratic equation \( x^2 - 6x - 20 = 20 \) by completing the square, we first move all terms to one side of the equation:

\[
x^2 - 6x - 20 - 20 = 0
\]

This simplifies to:

\[
x^2 - 6x - 40 = 0
\]

Next, we complete the square for the quadratic expression \( x^2 - 6x \).

1. Take the coefficient of \( x \), which is \(-6\), divide it by 2, and square it:

\[
\left(\frac{-6}{2}\right)^2 = (-3)^2 = 9
\]

2. Add and subtract \( 9 \) in the equation:

\[
x^2 - 6x + 9 - 9 - 40 = 0
\]

This can be rewritten as:

\[
(x - 3)^2 - 49 = 0
\]

3. Move the constant term to the other side:

\[
(x - 3)^2 = 49
\]

4. Take the square root of both sides:

\[
x - 3 = 7 \quad \text{or} \quad x - 3 = -7
\]

5. Solve for \( x \):

\[
x = 10 \quad \text{or} \quad x = -4
\]

So the solutions to the equation are:

\[
x = 10, \quad x = -4
\]

Thus the correct response is:

**x=10, x=−4**.