Question

what are the solutions to the quadratic equation $4x^2 = 64$?\
\bigcirc $x = -16$ and $x = 16$\
\bigcirc $x = -8$ and $x = 8$\
\bigcirc $x = -4$ and $x = 4$\
\bigcirc $x = -2$ and $x = 2$

Explanation:

Step1: Divide both sides by 4

To isolate \( x^2 \), we divide both sides of the equation \( 4x^2 = 64 \) by 4.
\[
\frac{4x^2}{4} = \frac{64}{4}
\]
This simplifies to:
\[
x^2 = 16
\]

Step2: Take square root of both sides

To solve for \( x \), we take the square root of both sides of the equation \( x^2 = 16 \). Remember that when we take the square root of a number, we consider both the positive and negative roots.
\[
x = \pm\sqrt{16}
\]
Since \( \sqrt{16} = 4 \), we have:
\[
x = \pm 4
\]
This means \( x = 4 \) or \( x = -4 \).

Answer:

C. \( x = -4 \) and \( x = 4 \) (assuming the options are labeled as A, B, C, D with C being \( x = -4 \) and \( x = 4 \))