# Problem of the Week

## Updated at Jan 24, 2022 8:49 AM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation $$4\times \frac{5}{{(2+t)}^{2}}=\frac{20}{49}$$?

Check out the solution below!

$4\times \frac{5}{{(2+t)}^{2}}=\frac{20}{49}$

 1 Simplify  $$4\times \frac{5}{{(2+t)}^{2}}$$  to  $$\frac{20}{{(2+t)}^{2}}$$.$\frac{20}{{(2+t)}^{2}}=\frac{20}{49}$2 Multiply both sides by $${(2+t)}^{2}$$.$20=\frac{20}{49}{(2+t)}^{2}$3 Simplify  $$\frac{20}{49}{(2+t)}^{2}$$  to  $$\frac{20{(2+t)}^{2}}{49}$$.$20=\frac{20{(2+t)}^{2}}{49}$4 Multiply both sides by $$49$$.$20\times 49=20{(2+t)}^{2}$5 Simplify  $$20\times 49$$  to  $$980$$.$980=20{(2+t)}^{2}$6 Divide both sides by $$20$$.$\frac{980}{20}={(2+t)}^{2}$7 Simplify  $$\frac{980}{20}$$  to  $$49$$.$49={(2+t)}^{2}$8 Take the square root of both sides.$\pm \sqrt{49}=2+t$9 Since $$7\times 7=49$$, the square root of $$49$$ is $$7$$.$\pm 7=2+t$10 Switch sides.$2+t=\pm 7$11 Break down the problem into these 2 equations.$2+t=7$$2+t=-7$12 Solve the 1st equation: $$2+t=7$$.1 Subtract $$2$$ from both sides.$t=7-2$2 Simplify  $$7-2$$  to  $$5$$.$t=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$t=5$13 Solve the 2nd equation: $$2+t=-7$$.1 Subtract $$2$$ from both sides.$t=-7-2$2 Simplify  $$-7-2$$  to  $$-9$$.$t=-9$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$t=-9$14 Collect all solutions.$t=5,-9$Donet=5,-9