SOLUTION: Solve by using quadratic formula: 4x squared minus 4 x equals -15.

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Question 209757: Solve by using quadratic formula: 4x squared minus 4 x equals -15.
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-4x=-15 Start with the given equation.


4x%5E2-4x%2B15=0 Get every term to the left side.


Notice that the quadratic 4x%5E2-4x%2B15 is in the form of Ax%5E2%2BBx%2BC where A=4, B=-4, and C=15


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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%2815%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-4, and C=15


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%284%29%2815%29+%29%29%2F%282%284%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%284%29%2815%29+%29%29%2F%282%284%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-240+%29%29%2F%282%284%29%29 Multiply 4%284%29%2815%29 to get 240


x+=+%284+%2B-+sqrt%28+-224+%29%29%2F%282%284%29%29 Subtract 240 from 16 to get -224


x+=+%284+%2B-+sqrt%28+-224+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%284+%2B-+4i%2Asqrt%2814%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%284%2B4i%2Asqrt%2814%29%29%2F%288%29 or x+=+%284-4i%2Asqrt%2814%29%29%2F%288%29 Break up the expression.


So the solutions are x+=+%284%2B4i%2Asqrt%2814%29%29%2F%288%29 or x+=+%284-4i%2Asqrt%2814%29%29%2F%288%29


Note: if you have no idea what the 'i' term is, chances are you haven't covered imaginary numbers yet. If so, then there are no solutions. Also, if you weren't expecting this solution, I'd double check the problem.