Question

harion wrote the equation $a = 18(x^{2}+1)$ to find the area of a rectangle that has a length of $x^{2}+1$ and a width of 18. he solved for $x$ and got $x=pmsqrt{\frac{a}{18}-1}$. which of the following is an equivalent equation for $x$?
$x=pmsqrt{\frac{a - 18}{18}}$
$x=pmsqrt{\frac{a + 18}{18}}$
$x=pmsqrt{a - 36}$
$x=pmsqrt{a + 36}$

Explanation:

Step1: Start with the original area - length - width formula

Given $A = 18(x^{2}+1)$.

Step2: Divide both sides by 18

$\frac{A}{18}=x^{2}+1$.

Step3: Subtract 1 from both sides

$x^{2}=\frac{A}{18}-1=\frac{A - 18}{18}$.

Step4: Take the square - root of both sides

$x=\pm\sqrt{\frac{A - 18}{18}}$.

Answer:

$x=\pm\sqrt{\frac{A - 18}{18}}$