# 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
$q=\frac{-16+8\sqrt{95}}{-32},\frac{-16-8\sqrt{95}}{-32}$

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