SOLUTION: I need help to find all real or imaginary solutions to each equation. -x^2 + x + 12 = 0

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Question 309975: I need help to find all real or imaginary solutions to each equation.
-x^2 + x + 12 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-x%5E2%2Bx%2B12=0 Start with the given equation.


Notice that the quadratic -x%5E2%2Bx%2B12 is in the form of Ax%5E2%2BBx%2BC where A=-1, B=1, and C=12


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-%281%29+%2B-+sqrt%28+%281%29%5E2-4%28-1%29%2812%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=1, and C=12


x+=+%28-1+%2B-+sqrt%28+1-4%28-1%29%2812%29+%29%29%2F%282%28-1%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--48+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%2812%29 to get -48


x+=+%28-1+%2B-+sqrt%28+1%2B48+%29%29%2F%282%28-1%29%29 Rewrite sqrt%281--48%29 as sqrt%281%2B48%29


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%282%28-1%29%29 Add 1 to 48 to get 49


x+=+%28-1+%2B-+sqrt%28+49+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%28-1+%2B-+7%29%2F%28-2%29 Take the square root of 49 to get 7.


x+=+%28-1+%2B+7%29%2F%28-2%29 or x+=+%28-1+-+7%29%2F%28-2%29 Break up the expression.


x+=+%286%29%2F%28-2%29 or x+=++%28-8%29%2F%28-2%29 Combine like terms.


x+=+-3 or x+=+4 Simplify.


So the solutions are x+=+-3 or x+=+4