Problem of the Week

Updated at Nov 18, 2024 12:25 PM

This week's problem comes from the equation category.

How would you solve the equation (4−2(3−t))2=36{(4-2(3-t))}^{2}=36?

Let's begin!



(4−2(3−t))2=36{(4-2(3-t))}^{2}=36

1
Factor out the common term 22.
(2(2−3+t))2=36{(2(2-3+t))}^{2}=36

2
Simplify  2−3+t2-3+t  to  t−1t-1.
(2(t−1))2=36{(2(t-1))}^{2}=36

3
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
22(t−1)2=36{2}^{2}{(t-1)}^{2}=36

4
Simplify  22{2}^{2}  to  44.
4(t−1)2=364{(t-1)}^{2}=36

5
Divide both sides by 44.
(t−1)2=364{(t-1)}^{2}=\frac{36}{4}

6
Simplify  364\frac{36}{4}  to  99.
(t−1)2=9{(t-1)}^{2}=9

7
Take the square root of both sides.
t−1=±9t-1=\pm \sqrt{9}

8
Since 3×3=93\times 3=9, the square root of 99 is 33.
t−1=±3t-1=\pm 3

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

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

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

12
Collect all solutions.
t=4,−2t=4,-2

Done
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