# Problem of the Week

## Updated at Jul 26, 2021 11:02 AM

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

Below is the solution.

$6{(\frac{n-3}{2})}^{2}=6$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$6\times \frac{{(n-3)}^{2}}{{2}^{2}}=6$2 Simplify  $${2}^{2}$$  to  $$4$$.$6\times \frac{{(n-3)}^{2}}{4}=6$3 Simplify  $$6\times \frac{{(n-3)}^{2}}{4}$$  to  $$\frac{3{(n-3)}^{2}}{2}$$.$\frac{3{(n-3)}^{2}}{2}=6$4 Multiply both sides by $$2$$.$3{(n-3)}^{2}=6\times 2$5 Simplify  $$6\times 2$$  to  $$12$$.$3{(n-3)}^{2}=12$6 Divide both sides by $$3$$.${(n-3)}^{2}=\frac{12}{3}$7 Simplify  $$\frac{12}{3}$$  to  $$4$$.${(n-3)}^{2}=4$8 Take the square root of both sides.$n-3=\pm \sqrt{4}$9 Since $$2\times 2=4$$, the square root of $$4$$ is $$2$$.$n-3=\pm 2$10 Break down the problem into these 2 equations.$n-3=2$$n-3=-2$11 Solve the 1st equation: $$n-3=2$$.1 Add $$3$$ to both sides.$n=2+3$2 Simplify  $$2+3$$  to  $$5$$.$n=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$n=5$12 Solve the 2nd equation: $$n-3=-2$$.1 Add $$3$$ to both sides.$n=-2+3$2 Simplify  $$-2+3$$  to  $$1$$.$n=1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$n=1$13 Collect all solutions.$n=5,1$Done n=5,1