# Problem of the Week

## Updated at Apr 25, 2022 4:49 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation $${(2+q)}^{2}\times \frac{5}{4q}=\frac{45}{4}$$?

Check out the solution below!

${(2+q)}^{2}\times \frac{5}{4q}=\frac{45}{4}$

 1 Use this rule: $$a \times \frac{b}{c}=\frac{ab}{c}$$.$\frac{{(2+q)}^{2}\times 5}{4q}=\frac{45}{4}$2 Regroup terms.$\frac{5{(2+q)}^{2}}{4q}=\frac{45}{4}$3 Multiply both sides by $$4q$$.$5{(2+q)}^{2}=\frac{45}{4}\times 4q$4 Cancel $$4$$.$5{(2+q)}^{2}=45q$5 Divide both sides by $$5$$.${(2+q)}^{2}=9q$6 Expand.$4+4q+{q}^{2}=9q$7 Move all terms to one side.$4+4q+{q}^{2}-9q=0$8 Simplify  $$4+4q+{q}^{2}-9q$$  to  $$4-5q+{q}^{2}$$.$4-5q+{q}^{2}=0$9 Factor $$4-5q+{q}^{2}$$.1 Ask: Which two numbers add up to $$-5$$ and multiply to $$4$$?$$-4$$ and $$-1$$2 Rewrite the expression using the above.$(q-4)(q-1)$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$(q-4)(q-1)=0$10 Solve for $$q$$.1 Ask: When will $$(q-4)(q-1)$$ equal zero?When $$q-4=0$$ or $$q-1=0$$2 Solve each of the 2 equations above.$q=4,1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$q=4,1$Done q=4,1