# Problem of the Week

Updated at Nov 19, 2018 1:37 PM

How would you solve the equation $$\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}$$?

Below is the solution.

$\frac{{(4u)}^{2}}{5}+2=\frac{74}{5}$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$$\frac{{4}^{2}{u}^{2}}{5}+2=\frac{74}{5}$2 Simplify $${4}^{2}$$ to $$16$$$\frac{16{u}^{2}}{5}+2=\frac{74}{5}$3 Subtract $$2$$ from both sides$\frac{16{u}^{2}}{5}=\frac{74}{5}-2$4 Simplify $$\frac{74}{5}-2$$ to $$\frac{64}{5}$$$\frac{16{u}^{2}}{5}=\frac{64}{5}$5 Multiply both sides by $$5$$$16{u}^{2}=\frac{64}{5}\times 5$6 Simplify $$\frac{64}{5}\times 5$$ to $$\frac{320}{5}$$$16{u}^{2}=\frac{320}{5}$7 Simplify $$\frac{320}{5}$$ to $$64$$$16{u}^{2}=64$8 Divide both sides by $$16$$${u}^{2}=\frac{64}{16}$9 Simplify $$\frac{64}{16}$$ to $$4$$${u}^{2}=4$10 Take the square root of both sides$u=\pm \sqrt{4}$11 Since $$2\times 2=4$$, the square root of $$4$$ is $$2$$$u=\pm 2$Doneu=2,-2