College Algebra, Chapter 1, 1.1, Section 1.1, Problem 94

Solve the equation $\displaystyle A = P \left( 1 + \frac{i}{100} \right)^2 $ for $i$

$
\begin{equation}
\begin{aligned}
A &= P \left( 1 + \frac{i}{100} \right)^2 && \text{Divide both sides by } P\\
\\
\frac{A}{P} &= \frac{\cancel{P}\left( 1 + \frac{i}{100} \right)^2}{\cancel{P}} && \text{Cancel out like terms}\\
\\
\frac{A}{P} &= \left( 1 + \frac{i}{100} \right)^2 && \text{Take the square root of both sides}\\
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\pm \sqrt{\frac{A}{P}} &= \sqrt{\left( 1 + \frac{i}{100} \right)^2} && \text{Simplify}\\
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\pm \sqrt{\frac{A}{P}} &= 1 + \frac{i}{100} && \text{Subtract both sides by 1}\\
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\pm \sqrt{\frac{A}{P}} -1 &= 1 + \frac{i}{100} -1 && \text{Simplify}\\
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\pm \sqrt{\frac{A}{P}} -1 &= \frac{i}{100} && \text{Multiply both sides by 100}\\
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100 & \left[ \pm \sqrt{\frac{A}{P}} - 1 = \frac{i}{\cancel{100}} \right] \cancel{100} && \text{Cancel out like terms}\\
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100 \left( \pm \sqrt{\frac{A}{P}} - 1 \right) &= i \\
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& \text{or}\\
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i &= 100 \left( \pm \sqrt{\frac{A}{P}} -1 \right)
\end{aligned}
\end{equation}
$