Problem of the Week

Updated at Apr 18, 2022 1:19 PM

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

How would you solve the equation \({(\frac{x-3}{2})}^{2}+6=\frac{25}{4}\)?

Check out the solution below!



\[{(\frac{x-3}{2})}^{2}+6=\frac{25}{4}\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{(x-3)}^{2}}{{2}^{2}}+6=\frac{25}{4}\]

2
Simplify  \({2}^{2}\)  to  \(4\).
\[\frac{{(x-3)}^{2}}{4}+6=\frac{25}{4}\]

3
Subtract \(6\) from both sides.
\[\frac{{(x-3)}^{2}}{4}=\frac{25}{4}-6\]

4
Simplify  \(\frac{25}{4}-6\)  to  \(\frac{1}{4}\).
\[\frac{{(x-3)}^{2}}{4}=\frac{1}{4}\]

5
Multiply both sides by \(4\).
\[{(x-3)}^{2}=\frac{1}{4}\times 4\]

6
Cancel \(4\).
\[{(x-3)}^{2}=1\]

7
Take the square root of both sides.
\[x-3=\pm \sqrt{1}\]

8
Simplify  \(\sqrt{1}\)  to  \(1\).
\[x-3=\pm 1\]

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

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

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

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

Done
Cymath foriOSAndroid