SOLUTION: What is a solution to the quadratic equation x^2+6x=-10

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Question 539374: What is a solution to the quadratic equation x^2+6x=-10
Answer by jim_thompson5910(35256) About Me  (Show Source):
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x%5E2%2B6x=-10 Start with the given equation.


x%5E2%2B6x%2B10=0 Get every term to the left side.


Notice that the quadratic x%5E2%2B6x%2B10 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=10


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%2810%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=10


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%2810%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-40+%29%29%2F%282%281%29%29 Multiply 4%281%29%2810%29 to get 40


x+=+%28-6+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 40 from 36 to get -4


x+=+%28-6+%2B-+sqrt%28+-4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%2Ai%29%2F%282%29 Take the square root of -4 to get 2%2Ai.


x+=+%28-6+%2B+2%2Ai%29%2F%282%29 or x+=+%28-6+-+2%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-6%29%2F%282%29+%2B+%282%2Ai%29%2F%282%29 or x+=++%28-6%29%2F%282%29+-+%282%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+-3%2Bi or x+=++-3-i Reduce.


So the solutions are x+=+-3%2Bi or x+=+-3-i


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