Problem of the Week

Updated at Apr 22, 2024 2:49 PM

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

How would you solve the equation (53−4p)2=25{(\frac{5}{3-4p})}^{2}=25?

Check out the solution below!



(53−4p)2=25{(\frac{5}{3-4p})}^{2}=25

1
Use Division Distributive Property: (xy)a=xaya{(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}.
52(3−4p)2=25\frac{{5}^{2}}{{(3-4p)}^{2}}=25

2
Simplify  52{5}^{2}  to  2525.
25(3−4p)2=25\frac{25}{{(3-4p)}^{2}}=25

3
Multiply both sides by (3−4p)2{(3-4p)}^{2}.
25=25(3−4p)225=25{(3-4p)}^{2}

4
Divide both sides by 2525.
1=(3−4p)21={(3-4p)}^{2}

5
Take the square root of both sides.
±1=3−4p\pm \sqrt{1}=3-4p

6
Simplify  1\sqrt{1}  to  11.
±1=3−4p\pm 1=3-4p

7
Switch sides.
3−4p=±13-4p=\pm 1

8
Break down the problem into these 2 equations.
3−4p=13-4p=1
3−4p=−13-4p=-1

9
Solve the 1st equation: 3−4p=13-4p=1.
p=12p=\frac{1}{2}

10
Solve the 2nd equation: 3−4p=−13-4p=-1.
p=1p=1

11
Collect all solutions.
p=12,1p=\frac{1}{2},1

Done

Decimal Form: 0.5, 1
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