Problem of the Week

Updated at May 31, 2021 5:46 PM

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

How would you solve the equation (4(z+2))26=96\frac{{(4(z+2))}^{2}}{6}=96?

Here are the steps:



(4(z+2))26=96\frac{{(4(z+2))}^{2}}{6}=96

1
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
42(z+2)26=96\frac{{4}^{2}{(z+2)}^{2}}{6}=96

2
Simplify  42{4}^{2}  to  1616.
16(z+2)26=96\frac{16{(z+2)}^{2}}{6}=96

3
Simplify  16(z+2)26\frac{16{(z+2)}^{2}}{6}  to  8(z+2)23\frac{8{(z+2)}^{2}}{3}.
8(z+2)23=96\frac{8{(z+2)}^{2}}{3}=96

4
Multiply both sides by 33.
8(z+2)2=96×38{(z+2)}^{2}=96\times 3

5
Simplify  96×396\times 3  to  288288.
8(z+2)2=2888{(z+2)}^{2}=288

6
Divide both sides by 88.
(z+2)2=2888{(z+2)}^{2}=\frac{288}{8}

7
Simplify  2888\frac{288}{8}  to  3636.
(z+2)2=36{(z+2)}^{2}=36

8
Take the square root of both sides.
z+2=±36z+2=\pm \sqrt{36}

9
Since 6×6=366\times 6=36, the square root of 3636 is 66.
z+2=±6z+2=\pm 6

10
Break down the problem into these 2 equations.
z+2=6z+2=6
z+2=−6z+2=-6

11
Solve the 1st equation: z+2=6z+2=6.
z=4z=4

12
Solve the 2nd equation: z+2=−6z+2=-6.
z=−8z=-8

13
Collect all solutions.
z=4,−8z=4,-8

Done
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