# 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$$\frac{y}{5}-3=-2$8 Solve the 1st equation: $$\frac{y}{5}-3=2$$.1 Add $$3$$ to both sides.$\frac{y}{5}=2+3$2 Simplify  $$2+3$$  to  $$5$$.$\frac{y}{5}=5$3 Multiply both sides by $$5$$.$y=5\times 5$4 Simplify  $$5\times 5$$  to  $$25$$.$y=25$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=25$9 Solve the 2nd equation: $$\frac{y}{5}-3=-2$$.1 Add $$3$$ to both sides.$\frac{y}{5}=-2+3$2 Simplify  $$-2+3$$  to  $$1$$.$\frac{y}{5}=1$3 Multiply both sides by $$5$$.$y=1\times 5$4 Simplify  $$1\times 5$$  to  $$5$$.$y=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=5$10 Collect all solutions.$y=25,5$Done y=25,5