# Problem of the Week

## Updated at Apr 18, 2022 1:19 PM

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

How would you solve the equation $${(\frac{x-3}{2})}^{2}+6=\frac{25}{4}$$?

Check out the solution below!

${(\frac{x-3}{2})}^{2}+6=\frac{25}{4}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{{(x-3)}^{2}}{{2}^{2}}+6=\frac{25}{4}$2 Simplify  $${2}^{2}$$  to  $$4$$.$\frac{{(x-3)}^{2}}{4}+6=\frac{25}{4}$3 Subtract $$6$$ from both sides.$\frac{{(x-3)}^{2}}{4}=\frac{25}{4}-6$4 Simplify  $$\frac{25}{4}-6$$  to  $$\frac{1}{4}$$.$\frac{{(x-3)}^{2}}{4}=\frac{1}{4}$5 Multiply both sides by $$4$$.${(x-3)}^{2}=\frac{1}{4}\times 4$6 Cancel $$4$$.${(x-3)}^{2}=1$7 Take the square root of both sides.$x-3=\pm \sqrt{1}$8 Simplify  $$\sqrt{1}$$  to  $$1$$.$x-3=\pm 1$9 Break down the problem into these 2 equations.$x-3=1$$x-3=-1$10 Solve the 1st equation: $$x-3=1$$.1 Add $$3$$ to both sides.$x=1+3$2 Simplify  $$1+3$$  to  $$4$$.$x=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=4$11 Solve the 2nd equation: $$x-3=-1$$.1 Add $$3$$ to both sides.$x=-1+3$2 Simplify  $$-1+3$$  to  $$2$$.$x=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=2$12 Collect all solutions.$x=4,2$Donex=4,2