Problem of the Week

Updated at Jun 8, 2020 11:44 AM

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

How would you solve $$6-{(3-\frac{5}{u})}^{2}=2$$?

Check out the solution below!

$6-{(3-\frac{5}{u})}^{2}=2$

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