Problem of the Week

Updated at Feb 3, 2020 12:10 PM

This week's problem comes from the equation category.

How would you solve the equation \({(4(y-3))}^{2}-6=58\)?

Let's begin!



\[{(4(y-3))}^{2}-6=58\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{4}^{2}{(y-3)}^{2}-6=58\]

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

3
Add \(6\) to both sides.
\[16{(y-3)}^{2}=58+6\]

4
Simplify  \(58+6\)  to  \(64\).
\[16{(y-3)}^{2}=64\]

5
Divide both sides by \(16\).
\[{(y-3)}^{2}=\frac{64}{16}\]

6
Simplify  \(\frac{64}{16}\)  to  \(4\).
\[{(y-3)}^{2}=4\]

7
Take the square root of both sides.
\[y-3=\pm \sqrt{4}\]

8
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[y-3=\pm 2\]

9
Break down the problem into these 2 equations.
\[y-3=2\]
\[y-3=-2\]

10
Solve the 1st equation: \(y-3=2\).
\[y=5\]

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

12
Collect all solutions.
\[y=5,1\]

Done
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