Question

Solve the quadratic equation x^2−96=4x
. (1 point)
Responses

x=−8, x=−12
x=−8, x=−12

x=−8, x=12
x=−8, x=12

x=−12, x=8
x=−12, x=8

x=8, x=12

Answer 1

To solve the quadratic equation \( x^2 - 96 = 4x \), we first rearrange it into standard form by moving all terms to one side:

\[
x^2 - 4x - 96 = 0
\]

Next, we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -4 \), and \( c = -96 \).

1. Calculate the discriminant:

\[
b^2 - 4ac = (-4)^2 - 4(1)(-96) = 16 + 384 = 400
\]

2. Apply the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{400}}{2(1)} = \frac{4 \pm 20}{2}
\]

3. This gives us two solutions:

\[
x = \frac{24}{2} = 12
\]

\[
x = \frac{-16}{2} = -8
\]

Thus, the solutions to the equation are \( x = -8 \) and \( x = 12 \).

The correct response is:

**x = −8, x = 12**