Problem of the Week

Updated at Jul 14, 2025 11:49 AM

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

How would you solve the equation 6−(33−u)2=1546-{(\frac{3}{3-u})}^{2}=\frac{15}{4}?

Check out the solution below!



6−(33−u)2=1546-{(\frac{3}{3-u})}^{2}=\frac{15}{4}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
6−32(3−u)2=1546-\frac{{3}^{2}}{{(3-u)}^{2}}=\frac{15}{4}

2
Simplify  32{3}^{2}  to  99.
6−9(3−u)2=1546-\frac{9}{{(3-u)}^{2}}=\frac{15}{4}

3
Subtract 66 from both sides.
−9(3−u)2=154−6-\frac{9}{{(3-u)}^{2}}=\frac{15}{4}-6

4
Simplify  154−6\frac{15}{4}-6  to  −94-\frac{9}{4}.
−9(3−u)2=−94-\frac{9}{{(3-u)}^{2}}=-\frac{9}{4}

5
Multiply both sides by (3−u)2{(3-u)}^{2}.
−9=−94(3−u)2-9=-\frac{9}{4}{(3-u)}^{2}

6
Simplify  94(3−u)2\frac{9}{4}{(3-u)}^{2}  to  9(3−u)24\frac{9{(3-u)}^{2}}{4}.
−9=−9(3−u)24-9=-\frac{9{(3-u)}^{2}}{4}

7
Multiply both sides by 44.
−9×4=−9(3−u)2-9\times 4=-9{(3-u)}^{2}

8
Simplify  −9×4-9\times 4  to  −36-36.
−36=−9(3−u)2-36=-9{(3-u)}^{2}

9
Divide both sides by −9-9.
−36−9=(3−u)2\frac{-36}{-9}={(3-u)}^{2}

10
Two negatives make a positive.
369=(3−u)2\frac{36}{9}={(3-u)}^{2}

11
Simplify  369\frac{36}{9}  to  44.
4=(3−u)24={(3-u)}^{2}

12
Take the square root of both sides.
±4=3−u\pm \sqrt{4}=3-u

13
Since 2×2=42\times 2=4, the square root of 44 is 22.
±2=3−u\pm 2=3-u

14
Switch sides.
3−u=±23-u=\pm 2

15
Break down the problem into these 2 equations.
3−u=23-u=2
3−u=−23-u=-2

16
Solve the 1st equation: 3−u=23-u=2.
u=1u=1

17
Solve the 2nd equation: 3−u=−23-u=-2.
u=5u=5

18
Collect all solutions.
u=1,5u=1,5

Done
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