Problem of the Week

Updated at Apr 18, 2022 1:19 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation (x−32)2+6=254{(\frac{x-3}{2})}^{2}+6=\frac{25}{4}?

Check out the solution below!



(x−32)2+6=254{(\frac{x-3}{2})}^{2}+6=\frac{25}{4}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
(x−3)222+6=254\frac{{(x-3)}^{2}}{{2}^{2}}+6=\frac{25}{4}

2
Simplify  22{2}^{2}  to  44.
(x−3)24+6=254\frac{{(x-3)}^{2}}{4}+6=\frac{25}{4}

3
Subtract 66 from both sides.
(x−3)24=254−6\frac{{(x-3)}^{2}}{4}=\frac{25}{4}-6

4
Simplify  254−6\frac{25}{4}-6  to  14\frac{1}{4}.
(x−3)24=14\frac{{(x-3)}^{2}}{4}=\frac{1}{4}

5
Multiply both sides by 44.
(x−3)2=14×4{(x-3)}^{2}=\frac{1}{4}\times 4

6
Cancel 44.
(x−3)2=1{(x-3)}^{2}=1

7
Take the square root of both sides.
x−3=±1x-3=\pm \sqrt{1}

8
Simplify  1\sqrt{1}  to  11.
x−3=±1x-3=\pm 1

9
Break down the problem into these 2 equations.
x−3=1x-3=1
x−3=−1x-3=-1

10
Solve the 1st equation: x−3=1x-3=1.
x=4x=4

11
Solve the 2nd equation: x−3=−1x-3=-1.
x=2x=2

12
Collect all solutions.
x=4,2x=4,2

Done
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