# Problem of the Week

## Updated at Aug 2, 2021 1:21 PM

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

How can we solve the equation $$\frac{4(v-3)(v-3)}{5}=\frac{4}{5}$$?

Here are the steps:

$\frac{4(v-3)(v-3)}{5}=\frac{4}{5}$

 1 Use Product Rule: $${x}^{a}{x}^{b}={x}^{a+b}$$.$\frac{4{(v-3)}^{2}}{5}=\frac{4}{5}$2 Multiply both sides by $$5$$.$4{(v-3)}^{2}=\frac{4}{5}\times 5$3 Cancel $$5$$.$4{(v-3)}^{2}=4$4 Divide both sides by $$4$$.${(v-3)}^{2}=1$5 Take the square root of both sides.$v-3=\pm \sqrt{1}$6 Simplify  $$\sqrt{1}$$  to  $$1$$.$v-3=\pm 1$7 Break down the problem into these 2 equations.$v-3=1$$v-3=-1$8 Solve the 1st equation: $$v-3=1$$.1 Add $$3$$ to both sides.$v=1+3$2 Simplify  $$1+3$$  to  $$4$$.$v=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$v=4$9 Solve the 2nd equation: $$v-3=-1$$.1 Add $$3$$ to both sides.$v=-1+3$2 Simplify  $$-1+3$$  to  $$2$$.$v=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$v=2$10 Collect all solutions.$v=4,2$Donev=4,2