Problem of the Week

Updated at Mar 11, 2019 2:33 PM

This week we have another equation problem:

How can we solve the equation \({(3(\frac{y}{5}-3))}^{2}=36\)?

Let's start!



\[{(3(\frac{y}{5}-3))}^{2}=36\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{3}^{2}{(\frac{y}{5}-3)}^{2}=36\]

2
Simplify \({3}^{2}\) to \(9\).
\[9{(\frac{y}{5}-3)}^{2}=36\]

3
Divide both sides by \(9\).
\[{(\frac{y}{5}-3)}^{2}=\frac{36}{9}\]

4
Simplify \(\frac{36}{9}\) to \(4\).
\[{(\frac{y}{5}-3)}^{2}=4\]

5
Take the square root of both sides.
\[\frac{y}{5}-3=\pm \sqrt{4}\]

6
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{y}{5}-3=\pm 2\]

7
Break down the problem into these 2 equations.
\[\frac{y}{5}-3=2\]
\[\frac{y}{5}-3=-2\]

8
How?
Solve the 1st equation: \(\frac{y}{5}-3=2\).
\[y=25\]

9
How?
Solve the 2nd equation: \(\frac{y}{5}-3=-2\).
\[y=5\]

10
Collect all solutions.
\[y=25,5\]

Done