# Problem of the Week

## Updated at Feb 3, 2020 12:10 PM

This week's problem comes from the equation category.

How would you solve the equation $${(4(y-3))}^{2}-6=58$$?

Let's begin!

${(4(y-3))}^{2}-6=58$

 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.${4}^{2}{(y-3)}^{2}-6=58$2 Simplify  $${4}^{2}$$  to  $$16$$.$16{(y-3)}^{2}-6=58$3 Add $$6$$ to both sides.$16{(y-3)}^{2}=58+6$4 Simplify  $$58+6$$  to  $$64$$.$16{(y-3)}^{2}=64$5 Divide both sides by $$16$$.${(y-3)}^{2}=\frac{64}{16}$6 Simplify  $$\frac{64}{16}$$  to  $$4$$.${(y-3)}^{2}=4$7 Take the square root of both sides.$y-3=\pm \sqrt{4}$8 Since $$2\times 2=4$$, the square root of $$4$$ is $$2$$.$y-3=\pm 2$9 Break down the problem into these 2 equations.$y-3=2$$y-3=-2$10 Solve the 1st equation: $$y-3=2$$.1 Add $$3$$ to both sides.$y=2+3$2 Simplify  $$2+3$$  to  $$5$$.$y=5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=5$11 Solve the 2nd equation: $$y-3=-2$$.1 Add $$3$$ to both sides.$y=-2+3$2 Simplify  $$-2+3$$  to  $$1$$.$y=1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$y=1$12 Collect all solutions.$y=5,1$Done y=5,1