Question

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

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 negative 10 , x equals 4

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

x=52
, x=−46

Answer 1

To solve the quadratic equation \( x^2 - 6x - 20 = 20 \) by completing the square, follow these steps:

1. Start by moving the constant term to the right side of the equation:

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

2. Rearrange the equation:

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

3. To complete the square, take half of the coefficient of \( x \) (which is -6), square it, and add it to both sides. Half of -6 is -3, and squaring it gives 9:

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

This simplifies to:

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

4. Now take the square root of both sides:

\[
x - 3 = \pm 7
\]

5. Solve for \( x \):

\[
x - 3 = 7 \implies x = 10
\]
\[
x - 3 = -7 \implies x = -4
\]

So the solutions to the equation are:

\[
x = 10 \text{ and } x = -4
\]

Therefore, the correct response is:

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