Problem of the Week

Updated at Dec 11, 2023 1:20 PM

This week's problem comes from the equation category.

How would you solve (45m−3)2=125{(\frac{4}{5}m-3)}^{2}=\frac{1}{25}?

Let's begin!



(45m−3)2=125{(\frac{4}{5}m-3)}^{2}=\frac{1}{25}

1
Simplify  45m\frac{4}{5}m  to  4m5\frac{4m}{5}.
(4m5−3)2=125{(\frac{4m}{5}-3)}^{2}=\frac{1}{25}

2
Take the square root of both sides.
4m5−3=±125\frac{4m}{5}-3=\pm \sqrt{\frac{1}{25}}

3
Simplify  125\sqrt{\frac{1}{25}}  to  125\frac{\sqrt{1}}{\sqrt{25}}.
4m5−3=±125\frac{4m}{5}-3=\pm \frac{\sqrt{1}}{\sqrt{25}}

4
Simplify  1\sqrt{1}  to  11.
4m5−3=±125\frac{4m}{5}-3=\pm \frac{1}{\sqrt{25}}

5
Since 5×5=255\times 5=25, the square root of 2525 is 55.
4m5−3=±15\frac{4m}{5}-3=\pm \frac{1}{5}

6
Break down the problem into these 2 equations.
4m5−3=15\frac{4m}{5}-3=\frac{1}{5}
4m5−3=−15\frac{4m}{5}-3=-\frac{1}{5}

7
Solve the 1st equation: 4m5−3=15\frac{4m}{5}-3=\frac{1}{5}.
m=4m=4

8
Solve the 2nd equation: 4m5−3=−15\frac{4m}{5}-3=-\frac{1}{5}.
m=72m=\frac{7}{2}

9
Collect all solutions.
m=4,72m=4,\frac{7}{2}

Done

Decimal Form: 4, 3.5
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