Problem of the Week

Updated at Mar 23, 2020 11:51 AM

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

How can we solve the equation \({(4z-4)}^{2}-6=58\)?

Here are the steps:



\[{(4z-4)}^{2}-6=58\]

1
Factor out the common term \(4\).
\[{(4(z-1))}^{2}-6=58\]

2
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{4}^{2}{(z-1)}^{2}-6=58\]

3
Simplify  \({4}^{2}\)  to  \(16\).
\[16{(z-1)}^{2}-6=58\]

4
Add \(6\) to both sides.
\[16{(z-1)}^{2}=58+6\]

5
Simplify  \(58+6\)  to  \(64\).
\[16{(z-1)}^{2}=64\]

6
Divide both sides by \(16\).
\[{(z-1)}^{2}=\frac{64}{16}\]

7
Simplify  \(\frac{64}{16}\)  to  \(4\).
\[{(z-1)}^{2}=4\]

8
Take the square root of both sides.
\[z-1=\pm \sqrt{4}\]

9
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[z-1=\pm 2\]

10
Break down the problem into these 2 equations.
\[z-1=2\]
\[z-1=-2\]

11
Solve the 1st equation: \(z-1=2\).
\[z=3\]

12
Solve the 2nd equation: \(z-1=-2\).
\[z=-1\]

13
Collect all solutions.
\[z=3,-1\]

Done
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