# Problem of the Week

## Updated at Mar 4, 2019 1:58 PM

This week we have another equation problem:

How would you solve the equation $$6{(\frac{5}{2+w})}^{2}=\frac{25}{6}$$?

Let's start!

$6{(\frac{5}{2+w})}^{2}=\frac{25}{6}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$6\times \frac{{5}^{2}}{{(2+w)}^{2}}=\frac{25}{6}$2 Simplify  $${5}^{2}$$  to  $$25$$.$6\times \frac{25}{{(2+w)}^{2}}=\frac{25}{6}$3 Simplify  $$6\times \frac{25}{{(2+w)}^{2}}$$  to  $$\frac{150}{{(2+w)}^{2}}$$.$\frac{150}{{(2+w)}^{2}}=\frac{25}{6}$4 Multiply both sides by $${(2+w)}^{2}$$.$150=\frac{25}{6}{(2+w)}^{2}$5 Simplify  $$\frac{25}{6}{(2+w)}^{2}$$  to  $$\frac{25{(2+w)}^{2}}{6}$$.$150=\frac{25{(2+w)}^{2}}{6}$6 Multiply both sides by $$6$$.$150\times 6=25{(2+w)}^{2}$7 Simplify  $$150\times 6$$  to  $$900$$.$900=25{(2+w)}^{2}$8 Divide both sides by $$25$$.$\frac{900}{25}={(2+w)}^{2}$9 Simplify  $$\frac{900}{25}$$  to  $$36$$.$36={(2+w)}^{2}$10 Take the square root of both sides.$\pm \sqrt{36}=2+w$11 Since $$6\times 6=36$$, the square root of $$36$$ is $$6$$.$\pm 6=2+w$12 Switch sides.$2+w=\pm 6$13 Break down the problem into these 2 equations.$2+w=6$$2+w=-6$14 Solve the 1st equation: $$2+w=6$$.1 Subtract $$2$$ from both sides.$w=6-2$2 Simplify  $$6-2$$  to  $$4$$.$w=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=4$15 Solve the 2nd equation: $$2+w=-6$$.1 Subtract $$2$$ from both sides.$w=-6-2$2 Simplify  $$-6-2$$  to  $$-8$$.$w=-8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=-8$16 Collect all solutions.$w=4,-8$Done w=4,-8