# 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$$2+w=-6$14 How?Solve the 1st equation: $$2+w=6$$.1 Subtract $$2$$ from both sides.$w=6-2$2 Simplify $$6-2$$ to $$4$$.$w=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=4$15 How?Solve the 2nd equation: $$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$Donew=4,-8