Problem of the Week

Updated at Jan 7, 2019 2:41 PM

For this week we've brought you this equation problem.

How would you solve \(4t-5-\frac{5}{t}=\frac{1}{2}\)?

Here are the steps:



\[4t-5-\frac{5}{t}=\frac{1}{2}\]

1
Multiply both sides by \(2t\).
\[8{t}^{2}-10t-10=t\]

2
Move all terms to one side.
\[8{t}^{2}-10t-10-t=0\]

3
Simplify \(8{t}^{2}-10t-10-t\) to \(8{t}^{2}-11t-10\).
\[8{t}^{2}-11t-10=0\]

4
How?
Split the second term in \(8{t}^{2}-11t-10\) into two terms.
\[8{t}^{2}+5t-16t-10=0\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[t(8t+5)-2(8t+5)=0\]

6
Factor out the common term \(8t+5\).
\[(8t+5)(t-2)=0\]

7
How?
Solve for \(t\).
\[t=-\frac{5}{8},2\]

Done

Decimal Form: -0.625, 2