Problem of the Week

Updated at Jul 26, 2021 11:02 AM

How would you solve 6(n−32)2=66{(\frac{n-3}{2})}^{2}=6?

Below is the solution.



6(n−32)2=66{(\frac{n-3}{2})}^{2}=6

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
6×(n−3)222=66\times \frac{{(n-3)}^{2}}{{2}^{2}}=6

2
Simplify  22{2}^{2}  to  44.
6×(n−3)24=66\times \frac{{(n-3)}^{2}}{4}=6

3
Simplify  6×(n−3)246\times \frac{{(n-3)}^{2}}{4}  to  3(n−3)22\frac{3{(n-3)}^{2}}{2}.
3(n−3)22=6\frac{3{(n-3)}^{2}}{2}=6

4
Multiply both sides by 22.
3(n−3)2=6×23{(n-3)}^{2}=6\times 2

5
Simplify  6×26\times 2  to  1212.
3(n−3)2=123{(n-3)}^{2}=12

6
Divide both sides by 33.
(n−3)2=123{(n-3)}^{2}=\frac{12}{3}

7
Simplify  123\frac{12}{3}  to  44.
(n−3)2=4{(n-3)}^{2}=4

8
Take the square root of both sides.
n−3=±4n-3=\pm \sqrt{4}

9
Since 2×2=42\times 2=4, the square root of 44 is 22.
n−3=±2n-3=\pm 2

10
Break down the problem into these 2 equations.
n−3=2n-3=2
n−3=−2n-3=-2

11
Solve the 1st equation: n−3=2n-3=2.
n=5n=5

12
Solve the 2nd equation: n−3=−2n-3=-2.
n=1n=1

13
Collect all solutions.
n=5,1n=5,1

Done
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