Problem of the Week

Updated at Jan 29, 2024 3:57 PM

How can we solve the equation \(\frac{{t}^{2}}{5}-\frac{t+2}{2}=\frac{1}{5}\)?

Below is the solution.



\[\frac{{t}^{2}}{5}-\frac{t+2}{2}=\frac{1}{5}\]

1
Multiply both sides by \(10\) (the LCM of \(5, 2\)).
\[2{t}^{2}-5(t+2)=2\]

2
Expand.
\[2{t}^{2}-5t-10=2\]

3
Move all terms to one side.
\[2{t}^{2}-5t-10-2=0\]

4
Simplify  \(2{t}^{2}-5t-10-2\)  to  \(2{t}^{2}-5t-12\).
\[2{t}^{2}-5t-12=0\]

5
Split the second term in \(2{t}^{2}-5t-12\) into two terms.
\[2{t}^{2}+3t-8t-12=0\]

6
Factor out common terms in the first two terms, then in the last two terms.
\[t(2t+3)-4(2t+3)=0\]

7
Factor out the common term \(2t+3\).
\[(2t+3)(t-4)=0\]

8
Solve for \(t\).
\[t=-\frac{3}{2},4\]

Done

Decimal Form: -1.5, 4
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