Problem of the Week

Updated at Nov 4, 2024 1:29 PM

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

How would you solve (5u)2+4×5u=859{(\frac{5}{u})}^{2}+4\times \frac{5}{u}=\frac{85}{9}?

Check out the solution below!



(5u)2+4×5u=859{(\frac{5}{u})}^{2}+4\times \frac{5}{u}=\frac{85}{9}

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
52u2+4×5u=859\frac{{5}^{2}}{{u}^{2}}+4\times \frac{5}{u}=\frac{85}{9}

2
Simplify  52{5}^{2}  to  2525.
25u2+4×5u=859\frac{25}{{u}^{2}}+4\times \frac{5}{u}=\frac{85}{9}

3
Simplify  4×5u4\times \frac{5}{u}  to  20u\frac{20}{u}.
25u2+20u=859\frac{25}{{u}^{2}}+\frac{20}{u}=\frac{85}{9}

4
Multiply both sides by the Least Common Denominator: 9u9u.
225u+180=85u\frac{225}{u}+180=85u

5
Multiply both sides by uu.
225+180u=85u2225+180u=85{u}^{2}

6
Move all terms to one side.
225+180u−85u2=0225+180u-85{u}^{2}=0

7
Factor out the common term 55.
5(45+36u−17u2)=05(45+36u-17{u}^{2})=0

8
Factor out the negative sign.
5×−(17u2−36u−45)=05\times -(17{u}^{2}-36u-45)=0

9
Divide both sides by 55.
−17u2+36u+45=0-17{u}^{2}+36u+45=0

10
Multiply both sides by −1-1.
17u2−36u−45=017{u}^{2}-36u-45=0

11
Split the second term in 17u2−36u−4517{u}^{2}-36u-45 into two terms.
17u2+15u−51u−45=017{u}^{2}+15u-51u-45=0

12
Factor out common terms in the first two terms, then in the last two terms.
u(17u+15)−3(17u+15)=0u(17u+15)-3(17u+15)=0

13
Factor out the common term 17u+1517u+15.
(17u+15)(u−3)=0(17u+15)(u-3)=0

14
Solve for uu.
u=−1517,3u=-\frac{15}{17},3

Done

Decimal Form: -0.882353, 3
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