To determine the correct answer, let’s solve the equation step by step:
The given equation is:
[tex]\[ 5.5x^2 = 352 \][/tex]
1. Isolate [tex]\( x^2 \)[/tex]:
To isolate [tex]\( x^2 \)[/tex], we need to divide both sides of the equation by 5.5:
[tex]\[
x^2 = \frac{352}{5.5}
\][/tex]
2. Simplify the fraction:
Divide 352 by 5.5:
[tex]\[
x^2 = 64
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], take the square root of both sides of the equation:
[tex]\[
x = \sqrt{64} \quad \text{or} \quad x = -\sqrt{64}
\][/tex]
[tex]\[
x = 8 \quad \text{or} \quad x = -8
\][/tex]
4. Interpret the solutions:
We have two solutions: [tex]\( x = 8 \)[/tex] and [tex]\( x = -8 \)[/tex].
Since side lengths cannot be negative in a real-world context such as this one, [tex]\( x = -8 \)[/tex] is not a reasonable solution. Therefore, the only reasonable side length is [tex]\( x = 8 \)[/tex].
Thus, the statement that best describes the solutions to this equation is:
The solutions are -8 and 8, but only 8 is a reasonable side length.
