# Problem of the Week

## Updated at Sep 18, 2023 11:42 AM

How can we solve the equation $$4(2+\frac{5}{{v}^{2}})=\frac{37}{4}$$?

Below is the solution.

$4(2+\frac{5}{{v}^{2}})=\frac{37}{4}$

 1 Divide both sides by $$4$$.$2+\frac{5}{{v}^{2}}=\frac{\frac{37}{4}}{4}$2 Simplify  $$\frac{\frac{37}{4}}{4}$$  to  $$\frac{37}{4\times 4}$$.$2+\frac{5}{{v}^{2}}=\frac{37}{4\times 4}$3 Simplify  $$4\times 4$$  to  $$16$$.$2+\frac{5}{{v}^{2}}=\frac{37}{16}$4 Subtract $$2$$ from both sides.$\frac{5}{{v}^{2}}=\frac{37}{16}-2$5 Simplify  $$\frac{37}{16}-2$$  to  $$\frac{5}{16}$$.$\frac{5}{{v}^{2}}=\frac{5}{16}$6 Multiply both sides by $${v}^{2}$$.$5=\frac{5}{16}{v}^{2}$7 Simplify  $$\frac{5}{16}{v}^{2}$$  to  $$\frac{5{v}^{2}}{16}$$.$5=\frac{5{v}^{2}}{16}$8 Multiply both sides by $$16$$.$5\times 16=5{v}^{2}$9 Simplify  $$5\times 16$$  to  $$80$$.$80=5{v}^{2}$10 Divide both sides by $$5$$.$\frac{80}{5}={v}^{2}$11 Simplify  $$\frac{80}{5}$$  to  $$16$$.$16={v}^{2}$12 Take the square root of both sides.$\pm \sqrt{16}=v$13 Since $$4\times 4=16$$, the square root of $$16$$ is $$4$$.$\pm 4=v$14 Switch sides.$v=\pm 4$Done v=4,-4