# Problem of the Week

## Updated at May 15, 2023 11:28 AM

This week we have another equation problem:

How would you solve the equation $${(\frac{w+2}{5}+2)}^{2}=9$$?

Let's start!

${(\frac{w+2}{5}+2)}^{2}=9$

 1 Take the square root of both sides.$\frac{w+2}{5}+2=\pm \sqrt{9}$2 Since $$3\times 3=9$$, the square root of $$9$$ is $$3$$.$\frac{w+2}{5}+2=\pm 3$3 Break down the problem into these 2 equations.$\frac{w+2}{5}+2=3$$\frac{w+2}{5}+2=-3$4 Solve the 1st equation: $$\frac{w+2}{5}+2=3$$.1 Subtract $$2$$ from both sides.$\frac{w+2}{5}=3-2$2 Simplify  $$3-2$$  to  $$1$$.$\frac{w+2}{5}=1$3 Multiply both sides by $$5$$.$w+2=1\times 5$4 Simplify  $$1\times 5$$  to  $$5$$.$w+2=5$5 Subtract $$2$$ from both sides.$w=5-2$6 Simplify  $$5-2$$  to  $$3$$.$w=3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=3$5 Solve the 2nd equation: $$\frac{w+2}{5}+2=-3$$.1 Subtract $$2$$ from both sides.$\frac{w+2}{5}=-3-2$2 Simplify  $$-3-2$$  to  $$-5$$.$\frac{w+2}{5}=-5$3 Multiply both sides by $$5$$.$w+2=-5\times 5$4 Simplify  $$5\times 5$$  to  $$25$$.$w+2=-25$5 Subtract $$2$$ from both sides.$w=-25-2$6 Simplify  $$-25-2$$  to  $$-27$$.$w=-27$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=-27$6 Collect all solutions.$w=3,-27$Done w=3,-27