Problem of the Week

Updated at Mar 23, 2020 11:51 AM

For this week we've brought you this equation problem.

How can we solve the equation $${(4z-4)}^{2}-6=58$$?

Here are the steps:

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

 1 Factor out the common term $$4$$.${(4(z-1))}^{2}-6=58$2 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.${4}^{2}{(z-1)}^{2}-6=58$3 Simplify  $${4}^{2}$$  to  $$16$$.$16{(z-1)}^{2}-6=58$4 Add $$6$$ to both sides.$16{(z-1)}^{2}=58+6$5 Simplify  $$58+6$$  to  $$64$$.$16{(z-1)}^{2}=64$6 Divide both sides by $$16$$.${(z-1)}^{2}=\frac{64}{16}$7 Simplify  $$\frac{64}{16}$$  to  $$4$$.${(z-1)}^{2}=4$8 Take the square root of both sides.$z-1=\pm \sqrt{4}$9 Since $$2\times 2=4$$, the square root of $$4$$ is $$2$$.$z-1=\pm 2$10 Break down the problem into these 2 equations.$z-1=2$$z-1=-2$11 Solve the 1st equation: $$z-1=2$$.1 Add $$1$$ to both sides.$z=2+1$2 Simplify  $$2+1$$  to  $$3$$.$z=3$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=3$12 Solve the 2nd equation: $$z-1=-2$$.1 Add $$1$$ to both sides.$z=-2+1$2 Simplify  $$-2+1$$  to  $$-1$$.$z=-1$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=-1$13 Collect all solutions.$z=3,-1$Donez=3,-1