SOLUTION: How would I solve for (x+8)^2 -7= -12 since you can't have the square root of a negetive number?

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Question 173310: How would I solve for (x+8)^2 -7= -12
since you can't have the square root of a negetive number?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%2B8%29%5E2-7=-12 Start with the given equation.


%28x%2B8%29%5E2=-12%2B7Add 7 to both sides.


%28x%2B8%29%5E2=-5 Combine like terms.


x%2B8=0%2B-sqrt%28-5%29 Take the square root of both sides.


x%2B8=sqrt%28-5%29 or x%2B8=-sqrt%28-5%29 Break up the "plus/minus" to form two equations.


x%2B8=sqrt%28-1%2A5%29 or x%2B8=-sqrt%28-1%2A5%29 Factor -5 into -1*5


x%2B8=sqrt%28-1%29%2Asqrt%285%29 or x%2B8=-sqrt%28-1%29%2Asqrt%285%29 Break up the square root.


x%2B8=i%2Asqrt%285%29 or x%2B8=-i%2Asqrt%285%29 Replace sqrt%28-1%29 with "i". Note: i=sqrt%28-1%29


x=-8%2Bi%2Asqrt%285%29 or x=-8-i%2Asqrt%285%29 Subtract 8 from both sides.


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Answer:


So the solutions are x=-8%2Bi%2Asqrt%285%29 or x=-8-i%2Asqrt%285%29.