Complete the square to solve the following quadratic equation: x^2−6x−20=20 .(1 point) Responses x=10 , x=−4 x equals 10 , x equals negative 4 x=−10 , x=4 x equals negative 10 , x equals 4 x=52 , x=−46 x equals 52 , x equals negative 46 x=3+210−−√, 3−210−−√

Answer 1

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

1. Move all terms to one side of the equation:

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

   This simplifies to:

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

2. Isolate the quadratic and linear terms:

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

3. Complete the square:

   To complete the square, take the coefficient of \( x \) (which is \(-6\)), divide it by 2, and square it:

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

   Add this square to both sides:

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

   This simplifies to:

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

4. Take the square root of both sides:

   \[ x - 3 = \pm 7 \]

5. Solve for \( x \):

   This gives us two equations:

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

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

Thus, the solution to the quadratic equation is:

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

The correct response is:

x equals 10, x equals negative 4.