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

Question

Responses

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
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, we first rearrange the equation:

1. Subtract 20 from both sides to set the equation to 0: \[ x^2 - 6x - 20 - 20 = 0 \implies x^2 - 6x - 40 = 0 \]

2. Next, we'll complete the square for the expression \(x^2 - 6x\). To do this, take half of the coefficient of \(x\), square it, and then add and subtract it. The coefficient of \(x\) is \(-6\):

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

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

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

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

6. Solving for \(x\):

   • For \(x - 3 = 7\): \[ x = 10 \]
   • For \(x - 3 = -7\): \[ x = -4 \]

Therefore, the solutions to the equation are \(x = 10\) and \(x = -4\).

The correct response is: x=10, x=−4 (or x equals 10 , x equals negative 4).