Problem of the Week

Updated at Oct 7, 2024 1:41 PM

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

How would you solve \(7+4w+\frac{5}{w}=\frac{97}{4}\)?

Here are the steps:



\[7+4w+\frac{5}{w}=\frac{97}{4}\]

1
Multiply both sides by \(4w\).
\[28w+16{w}^{2}+20=97w\]

2
Move all terms to one side.
\[28w+16{w}^{2}+20-97w=0\]

3
Simplify  \(28w+16{w}^{2}+20-97w\)  to  \(-69w+16{w}^{2}+20\).
\[-69w+16{w}^{2}+20=0\]

4
Split the second term in \(-69w+16{w}^{2}+20\) into two terms.
\[16{w}^{2}-5w-64w+20=0\]

5
Factor out common terms in the first two terms, then in the last two terms.
\[w(16w-5)-4(16w-5)=0\]

6
Factor out the common term \(16w-5\).
\[(16w-5)(w-4)=0\]

7
Solve for \(w\).
\[w=\frac{5}{16},4\]

Done

Decimal Form: 0.3125, 4
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