solve a word problem

Question

seven times the square of the difference between a number and 5 is -63. Find the number(s) 

 

Solve this by using the square root property 

Answer 1

7(n-5)²=-63

(n-5)²=-9

√(n-5)²=√-9

+(n-5)=3√-1 where √-1=i, the imaginary number

(n-5)=3i

n-5=3i

n=5+3i and

-(n-5)=3i

-n+5=3i

-n=-5+3i

n=5-3i

there are two solutions: n=5+3i and n=5-3i