# Problem of the Week

## Updated at Jan 1, 2024 11:08 AM

This week we have another equation problem:

How would you solve $${({(m-3)}^{2}+6)}^{2}=49$$?

Let's start!

${({(m-3)}^{2}+6)}^{2}=49$

 1 Take the square root of both sides.${(m-3)}^{2}+6=\pm \sqrt{49}$2 Since $$7\times 7=49$$, the square root of $$49$$ is $$7$$.${(m-3)}^{2}+6=\pm 7$3 Break down the problem into these 2 equations.${(m-3)}^{2}+6=7$${(m-3)}^{2}+6=-7$4 Solve the 1st equation: $${(m-3)}^{2}+6=7$$.1 Subtract $$6$$ from both sides.${(m-3)}^{2}=7-6$2 Simplify  $$7-6$$  to  $$1$$.${(m-3)}^{2}=1$3 Take the square root of both sides.$m-3=\pm \sqrt{1}$4 Simplify  $$\sqrt{1}$$  to  $$1$$.$m-3=\pm 1$5 Break down the problem into these 2 equations.$m-3=1$$m-3=-1$6 Solve the 1st equation: $$m-3=1$$.1 Add $$3$$ to both sides.$m=1+3$2 Simplify  $$1+3$$  to  $$4$$.$m=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=4$7 Solve the 2nd equation: $$m-3=-1$$.1 Add $$3$$ to both sides.$m=-1+3$2 Simplify  $$-1+3$$  to  $$2$$.$m=2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=2$8 Collect all solutions.$m=4,2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=4,2$5 Solve the 2nd equation: $${(m-3)}^{2}+6=-7$$.1 Subtract $$6$$ from both sides.${(m-3)}^{2}=-7-6$2 Simplify  $$-7-6$$  to  $$-13$$.${(m-3)}^{2}=-13$3 Take the square root of both sides.$m-3=\pm \sqrt{-13}$4 Simplify  $$\sqrt{-13}$$  to  $$\sqrt{13}\imath$$.$m-3=\pm \sqrt{13}\imath$5 Break down the problem into these 2 equations.$m-3=\sqrt{13}\imath$$m-3=-\sqrt{13}\imath$6 Solve the 1st equation: $$m-3=\sqrt{13}\imath$$.1 Add $$3$$ to both sides.$m=\sqrt{13}\imath +3$2 Regroup terms.$m=3+\sqrt{13}\imath$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=3+\sqrt{13}\imath$7 Solve the 2nd equation: $$m-3=-\sqrt{13}\imath$$.1 Add $$3$$ to both sides.$m=-\sqrt{13}\imath +3$2 Regroup terms.$m=3-\sqrt{13}\imath$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=3-\sqrt{13}\imath$8 Collect all solutions.$m=3+\sqrt{13}\imath ,3-\sqrt{13}\imath$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$m=3+\sqrt{13}\imath ,3-\sqrt{13}\imath$6 Collect all solutions.$m=4,2,3+\sqrt{13}\imath ,3-\sqrt{13}\imath$Donem=4,2,3+sqrt(13)*IM,3-sqrt(13)*IM