Problem of the Week

Updated at May 31, 2021 5:46 PM

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

How would you solve the equation \(\frac{{(4(z+2))}^{2}}{6}=96\)?

Here are the steps:



\[\frac{{(4(z+2))}^{2}}{6}=96\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{4}^{2}{(z+2)}^{2}}{6}=96\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{16{(z+2)}^{2}}{6}=96\]

3
Simplify  \(\frac{16{(z+2)}^{2}}{6}\)  to  \(\frac{8{(z+2)}^{2}}{3}\).
\[\frac{8{(z+2)}^{2}}{3}=96\]

4
Multiply both sides by \(3\).
\[8{(z+2)}^{2}=96\times 3\]

5
Simplify  \(96\times 3\)  to  \(288\).
\[8{(z+2)}^{2}=288\]

6
Divide both sides by \(8\).
\[{(z+2)}^{2}=\frac{288}{8}\]

7
Simplify  \(\frac{288}{8}\)  to  \(36\).
\[{(z+2)}^{2}=36\]

8
Take the square root of both sides.
\[z+2=\pm \sqrt{36}\]

9
Since \(6\times 6=36\), the square root of \(36\) is \(6\).
\[z+2=\pm 6\]

10
Break down the problem into these 2 equations.
\[z+2=6\]
\[z+2=-6\]

11
Solve the 1st equation: \(z+2=6\).
\[z=4\]

12
Solve the 2nd equation: \(z+2=-6\).
\[z=-8\]

13
Collect all solutions.
\[z=4,-8\]

Done
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