Complete the square to solve the following quadratic equation: x2−6x−20=20(1 point)Responsesx=52, x=−46x=52, x=−46x=−10, x=4x=−10, x=4x=10, x=−4x=10, x=−4x=3+210−−√, 3−210−−√

Answer 1

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

1. First, move everything to one side of the equation: \[ x^2 - 6x - 20 - 20 = 0 \implies x^2 - 6x - 40 = 0 \]

2. Now, we want to complete the square. Take the coefficient of \(x\) (which is \(-6\)), divide it by \(2\), and square it:

   • Coefficient of \(x\) is \(-6\).
   • Half of \(-6\) is \(-3\).
   • Squaring \(-3\) gives \(9\).

3. Add and subtract \(9\) inside the equation: \[ x^2 - 6x + 9 - 9 - 40 = 0 \] This can be rewritten as: \[ (x - 3)^2 - 49 = 0 \]

4. Rearranging gives: \[ (x - 3)^2 = 49 \]

5. Now, take the square root of both sides: \[ x - 3 = \pm 7 \]

6. Solve for \(x\):

   • \(x - 3 = 7 \implies x = 10\)
   • \(x - 3 = -7 \implies x = -4\)

So, the solutions to the original equation are: \[ x = 10 \quad \text{and} \quad x = -4 \]

Thus, the correct response from the given options is \(x = 10, x = -4\).