# Problem of the Week

## Updated at Jul 24, 2023 10:51 AM

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

How can we solve the equation $$5+\frac{6}{{(2+w)}^{2}}=\frac{31}{6}$$?

Here are the steps:

$5+\frac{6}{{(2+w)}^{2}}=\frac{31}{6}$

 1 Subtract $$5$$ from both sides.$\frac{6}{{(2+w)}^{2}}=\frac{31}{6}-5$2 Simplify  $$\frac{31}{6}-5$$  to  $$\frac{1}{6}$$.$\frac{6}{{(2+w)}^{2}}=\frac{1}{6}$3 Multiply both sides by $${(2+w)}^{2}$$.$6=\frac{1}{6}{(2+w)}^{2}$4 Simplify  $$\frac{1}{6}{(2+w)}^{2}$$  to  $$\frac{{(2+w)}^{2}}{6}$$.$6=\frac{{(2+w)}^{2}}{6}$5 Multiply both sides by $$6$$.$6\times 6={(2+w)}^{2}$6 Simplify  $$6\times 6$$  to  $$36$$.$36={(2+w)}^{2}$7 Take the square root of both sides.$\pm \sqrt{36}=2+w$8 Since $$6\times 6=36$$, the square root of $$36$$ is $$6$$.$\pm 6=2+w$9 Switch sides.$2+w=\pm 6$10 Break down the problem into these 2 equations.$2+w=6$$2+w=-6$11 Solve the 1st equation: $$2+w=6$$.1 Subtract $$2$$ from both sides.$w=6-2$2 Simplify  $$6-2$$  to  $$4$$.$w=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=4$12 Solve the 2nd equation: $$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$13 Collect all solutions.$w=4,-8$Donew=4,-8