Problem of the Week

Updated at Jul 25, 2022 10:33 AM

This week we have another equation problem:

How can we solve the equation \(4+4{(3-q)}^{2}=8\)?

Let's start!



\[4+4{(3-q)}^{2}=8\]

1
Subtract \(4\) from both sides.
\[4{(3-q)}^{2}=8-4\]

2
Simplify  \(8-4\)  to  \(4\).
\[4{(3-q)}^{2}=4\]

3
Divide both sides by \(4\).
\[{(3-q)}^{2}=1\]

4
Take the square root of both sides.
\[3-q=\pm \sqrt{1}\]

5
Simplify  \(\sqrt{1}\)  to  \(1\).
\[3-q=\pm 1\]

6
Break down the problem into these 2 equations.
\[3-q=1\]
\[3-q=-1\]

7
Solve the 1st equation: \(3-q=1\).
\[q=2\]

8
Solve the 2nd equation: \(3-q=-1\).
\[q=4\]

9
Collect all solutions.
\[q=2,4\]

Done
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