Problem of the Week

Updated at Apr 10, 2023 9:06 AM

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

How can we solve the equation \({(4q)}^{2}-\frac{5}{3-q}=59\)?

Here are the steps:



\[{(4q)}^{2}-\frac{5}{3-q}=59\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{4}^{2}{q}^{2}-\frac{5}{3-q}=59\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[16{q}^{2}-\frac{5}{3-q}=59\]

3
Multiply both sides by \(3-q\).
\[16{q}^{2}(3-q)-5=59(3-q)\]

4
Simplify.
\[48{q}^{2}-16{q}^{3}-5=177-59q\]

5
Move all terms to one side.
\[48{q}^{2}-16{q}^{3}-5-177+59q=0\]

6
Simplify  \(48{q}^{2}-16{q}^{3}-5-177+59q\)  to  \(48{q}^{2}-16{q}^{3}-182+59q\).
\[48{q}^{2}-16{q}^{3}-182+59q=0\]

7
Factor \(48{q}^{2}-16{q}^{3}-182+59q\) using Polynomial Division.
\[(-16{q}^{2}+16q+91)(q-2)=0\]

8
Solve for \(q\).
\[q=2\]

9
Use the Quadratic Formula.
\[q=\frac{-16+8\sqrt{95}}{-32},\frac{-16-8\sqrt{95}}{-32}\]

10
Collect all solutions from the previous steps.
\[q=2,\frac{-16+8\sqrt{95}}{-32},\frac{-16-8\sqrt{95}}{-32}\]

11
Simplify solutions.
\[q=2,\frac{2-\sqrt{95}}{4},\frac{2+\sqrt{95}}{4}\]

Done

Decimal Form: 2, -1.936699, 2.936699
Cymath foriOSAndroid