# Problem of the Week

## Updated at Jul 25, 2022 10:33 AM

This week we have another equation problem:

How can we solve the equation $$4+4{(3-q)}^{2}=8$$?

Let's start!

$4+4{(3-q)}^{2}=8$

 1 Subtract $$4$$ from both sides.$4{(3-q)}^{2}=8-4$2 Simplify  $$8-4$$  to  $$4$$.$4{(3-q)}^{2}=4$3 Divide both sides by $$4$$.${(3-q)}^{2}=1$4 Take the square root of both sides.$3-q=\pm \sqrt{1}$5 Simplify  $$\sqrt{1}$$  to  $$1$$.$3-q=\pm 1$6 Break down the problem into these 2 equations.$3-q=1$$3-q=-1$7 Solve the 1st equation: $$3-q=1$$.1 Subtract $$3$$ from both sides.$-q=1-3$2 Simplify  $$1-3$$  to  $$-2$$.$-q=-2$3 Multiply both sides by $$-1$$.$q=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$q=2$8 Solve the 2nd equation: $$3-q=-1$$.1 Subtract $$3$$ from both sides.$-q=-1-3$2 Simplify  $$-1-3$$  to  $$-4$$.$-q=-4$3 Multiply both sides by $$-1$$.$q=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$q=4$9 Collect all solutions.$q=2,4$Doneq=2,4