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=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

Answer 1

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

1. First, move the 20 to the left side of the equation:

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

   which simplifies to:

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

2. Next, isolate the \(x^2 - 6x\) term:

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

3. Now, complete the square. Take the coefficient of \(x\) (which is -6), divide it by 2 (resulting in -3), and then square it (resulting in 9). Add 9 to both sides:

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

   This simplifies to:

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

4. Now, take the square root of both sides:

   \[ x - 3 = \pm 7 \]

5. Solve for \(x\):

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

   and

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

Thus, the solutions to the equation \(x^2 - 6x - 20 = 20\) are:

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

This corresponds to the choice:

x=10 , x=−4