Question 173310


{{{(x+8)^2-7=-12}}} Start with the given equation.



{{{(x+8)^2=-12+7}}}Add {{{7}}} to both sides.



{{{(x+8)^2=-5}}} Combine like terms.



{{{x+8=0+-sqrt(-5)}}} Take the square root of both sides.



{{{x+8=sqrt(-5)}}} or {{{x+8=-sqrt(-5)}}} Break up the "plus/minus" to form two equations.



{{{x+8=sqrt(-1*5)}}} or {{{x+8=-sqrt(-1*5)}}} Factor -5 into -1*5



{{{x+8=sqrt(-1)*sqrt(5)}}} or {{{x+8=-sqrt(-1)*sqrt(5)}}} Break up the square root.



{{{x+8=i*sqrt(5)}}} or {{{x+8=-i*sqrt(5)}}} Replace {{{sqrt(-1)}}} with "i". Note: {{{i=sqrt(-1)}}}



{{{x=-8+i*sqrt(5)}}} or {{{x=-8-i*sqrt(5)}}} Subtract {{{8}}} from both sides.



--------------------------------------



Answer:



So the solutions are {{{x=-8+i*sqrt(5)}}} or {{{x=-8-i*sqrt(5)}}}.