# Problem of the Week

## Updated at Dec 9, 2019 2:25 PM

This week's problem comes from the equation category.

How would you solve the equation $${(4\times \frac{5}{2+w})}^{2}=25$$?

Let's begin!

${(4\times \frac{5}{2+w})}^{2}=25$

 1 Simplify  $$4\times \frac{5}{2+w}$$  to  $$\frac{20}{2+w}$$.${(\frac{20}{2+w})}^{2}=25$2 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{{20}^{2}}{{(2+w)}^{2}}=25$3 Simplify  $${20}^{2}$$  to  $$400$$.$\frac{400}{{(2+w)}^{2}}=25$4 Multiply both sides by $${(2+w)}^{2}$$.$400=25{(2+w)}^{2}$5 Divide both sides by $$25$$.$\frac{400}{25}={(2+w)}^{2}$6 Simplify  $$\frac{400}{25}$$  to  $$16$$.$16={(2+w)}^{2}$7 Take the square root of both sides.$\pm \sqrt{16}=2+w$8 Since $$4\times 4=16$$, the square root of $$16$$ is $$4$$.$\pm 4=2+w$9 Switch sides.$2+w=\pm 4$10 Break down the problem into these 2 equations.$2+w=4$$2+w=-4$11 Solve the 1st equation: $$2+w=4$$.1 Subtract $$2$$ from both sides.$w=4-2$2 Simplify  $$4-2$$  to  $$2$$.$w=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=2$12 Solve the 2nd equation: $$2+w=-4$$.1 Subtract $$2$$ from both sides.$w=-4-2$2 Simplify  $$-4-2$$  to  $$-6$$.$w=-6$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=-6$13 Collect all solutions.$w=2,-6$Done w=2,-6