# Problem of the Week

## Updated at Nov 11, 2019 2:40 PM

This week's problem comes from the equation category.

How would you solve the equation $$6+{(3(3-z))}^{2}=42$$?

Let's begin!

$6+{(3(3-z))}^{2}=42$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$6+{3}^{2}{(3-z)}^{2}=42$2 Simplify  $${3}^{2}$$  to  $$9$$.$6+9{(3-z)}^{2}=42$3 Subtract $$6$$ from both sides.$9{(3-z)}^{2}=42-6$4 Simplify  $$42-6$$  to  $$36$$.$9{(3-z)}^{2}=36$5 Divide both sides by $$9$$.${(3-z)}^{2}=\frac{36}{9}$6 Simplify  $$\frac{36}{9}$$  to  $$4$$.${(3-z)}^{2}=4$7 Take the square root of both sides.$3-z=\pm \sqrt{4}$8 Since $$2\times 2=4$$, the square root of $$4$$ is $$2$$.$3-z=\pm 2$9 Break down the problem into these 2 equations.$3-z=2$$3-z=-2$10 Solve the 1st equation: $$3-z=2$$.1 Subtract $$3$$ from both sides.$-z=2-3$2 Simplify  $$2-3$$  to  $$-1$$.$-z=-1$3 Multiply both sides by $$-1$$.$z=1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=1$11 Solve the 2nd equation: $$3-z=-2$$.1 Subtract $$3$$ from both sides.$-z=-2-3$2 Simplify  $$-2-3$$  to  $$-5$$.$-z=-5$3 Multiply both sides by $$-1$$.$z=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=5$12 Collect all solutions.$z=1,5$Donez=1,5