Let's solve the equation [tex]\( 72 = 2x^2 \)[/tex] step-by-step.
1. Isolate [tex]\( x^2 \)[/tex]:
- We start with the equation: [tex]\( 72 = 2x^2 \)[/tex].
- To isolate [tex]\( x^2 \)[/tex], divide both sides of the equation by 2:
[tex]\[
\frac{72}{2} = x^2
\][/tex]
- Simplifying the left-hand side, we get:
[tex]\[
36 = x^2
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
- To find [tex]\( x \)[/tex], we take the square root of both sides of the equation [tex]\( x^2 = 36 \)[/tex]:
[tex]\[
x = \sqrt{36}
\][/tex]
- The square root of 36 is 6, but we must consider both positive and negative roots because both values will satisfy the equation when squared:
[tex]\[
x = 6 \quad \text{and} \quad x = -6
\][/tex]
Therefore, the solutions to the equation [tex]\( 72 = 2x^2 \)[/tex] are [tex]\( x = 6 \)[/tex] and [tex]\( x = -6 \)[/tex].
So the correct answer to the given equation is:
(B) [tex]\( x = -6 \)[/tex] and [tex]\( x = 6 \)[/tex]
