Problem of the Week

Updated at Aug 2, 2021 1:21 PM

For this week we've brought you this equation problem.

How can we solve the equation \(\frac{4(v-3)(v-3)}{5}=\frac{4}{5}\)?

Here are the steps:



\[\frac{4(v-3)(v-3)}{5}=\frac{4}{5}\]

1
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{4{(v-3)}^{2}}{5}=\frac{4}{5}\]

2
Multiply both sides by \(5\).
\[4{(v-3)}^{2}=\frac{4}{5}\times 5\]

3
Cancel \(5\).
\[4{(v-3)}^{2}=4\]

4
Divide both sides by \(4\).
\[{(v-3)}^{2}=1\]

5
Take the square root of both sides.
\[v-3=\pm \sqrt{1}\]

6
Simplify  \(\sqrt{1}\)  to  \(1\).
\[v-3=\pm 1\]

7
Break down the problem into these 2 equations.
\[v-3=1\]
\[v-3=-1\]

8
Solve the 1st equation: \(v-3=1\).
\[v=4\]

9
Solve the 2nd equation: \(v-3=-1\).
\[v=2\]

10
Collect all solutions.
\[v=4,2\]

Done
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