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=−10, x=4
x equals negative 10 , x equals 4

x=10, x=−4
x equals 10 , x equals negative 4

x=3+210−−√, 3−210−−√

Answer 1

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

\[
x^2 - 6x - 20 - 20 = 0 \\
x^2 - 6x - 40 = 0
\]

Next, we can complete the square for the 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 this square inside the equation:

\[
x^2 - 6x + 9 - 9 - 40 = 0 \\
(x - 3)^2 - 49 = 0
\]

3. Now, isolate the square:

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

4. Take the square root of both sides:

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

5. Solve for \( x \):

\[
x = 3 + 7 \quad \Rightarrow \quad x = 10 \\
x = 3 - 7 \quad \Rightarrow \quad x = -4
\]

Thus, the solutions to the quadratic equation are:

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

Therefore, the correct response is:

**x=10, x=−4**
**x equals 10 , x equals negative 4**