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 \({(4-2(3-t))}^{2}=36\)?

Let's begin!



\[{(4-2(3-t))}^{2}=36\]

1
Factor out the common term \(2\).
\[{(2(2-3+t))}^{2}=36\]

2
Simplify  \(2-3+t\)  to  \(t-1\).
\[{(2(t-1))}^{2}=36\]

3
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{2}^{2}{(t-1)}^{2}=36\]

4
Simplify  \({2}^{2}\)  to  \(4\).
\[4{(t-1)}^{2}=36\]

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

6
Simplify  \(\frac{36}{4}\)  to  \(9\).
\[{(t-1)}^{2}=9\]

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

8
Since \(3\times 3=9\), the square root of \(9\) is \(3\).
\[t-1=\pm 3\]

9
Break down the problem into these 2 equations.
\[t-1=3\]
\[t-1=-3\]

10
Solve the 1st equation: \(t-1=3\).
\[t=4\]

11
Solve the 2nd equation: \(t-1=-3\).
\[t=-2\]

12
Collect all solutions.
\[t=4,-2\]

Done
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