-0.39x^2+12x-40=0

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Solution for -0.39x^2+12x-40=0 equation:


Simplifying
-0.39x2 + 12x + -40 = 0

Reorder the terms:
-40 + 12x + -0.39x2 = 0

Solving
-40 + 12x + -0.39x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.39 the coefficient of the squared term: 

Divide each side by '-0.39'.
102.5641026 + -30.76923077x + x2 = 0

Move the constant term to the right:

Add '-102.5641026' to each side of the equation.
102.5641026 + -30.76923077x + -102.5641026 + x2 = 0 + -102.5641026

Reorder the terms:
102.5641026 + -102.5641026 + -30.76923077x + x2 = 0 + -102.5641026

Combine like terms: 102.5641026 + -102.5641026 = 0.0000000
0.0000000 + -30.76923077x + x2 = 0 + -102.5641026
-30.76923077x + x2 = 0 + -102.5641026

Combine like terms: 0 + -102.5641026 = -102.5641026
-30.76923077x + x2 = -102.5641026

The x term is -30.76923077x.  Take half its coefficient (-15.38461539).
Square it (236.6863907) and add it to both sides.

Add '236.6863907' to each side of the equation.
-30.76923077x + 236.6863907 + x2 = -102.5641026 + 236.6863907

Reorder the terms:
236.6863907 + -30.76923077x + x2 = -102.5641026 + 236.6863907

Combine like terms: -102.5641026 + 236.6863907 = 134.1222881
236.6863907 + -30.76923077x + x2 = 134.1222881

Factor a perfect square on the left side:
(x + -15.38461539)(x + -15.38461539) = 134.1222881

Calculate the square root of the right side: 11.58111774

Break this problem into two subproblems by setting 
(x + -15.38461539) equal to 11.58111774 and -11.58111774.

Subproblem 1

x + -15.38461539 = 11.58111774 Simplifying x + -15.38461539 = 11.58111774 Reorder the terms: -15.38461539 + x = 11.58111774 Solving -15.38461539 + x = 11.58111774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.38461539' to each side of the equation. -15.38461539 + 15.38461539 + x = 11.58111774 + 15.38461539 Combine like terms: -15.38461539 + 15.38461539 = 0.00000000 0.00000000 + x = 11.58111774 + 15.38461539 x = 11.58111774 + 15.38461539 Combine like terms: 11.58111774 + 15.38461539 = 26.96573313 x = 26.96573313 Simplifying x = 26.96573313

Subproblem 2

x + -15.38461539 = -11.58111774 Simplifying x + -15.38461539 = -11.58111774 Reorder the terms: -15.38461539 + x = -11.58111774 Solving -15.38461539 + x = -11.58111774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.38461539' to each side of the equation. -15.38461539 + 15.38461539 + x = -11.58111774 + 15.38461539 Combine like terms: -15.38461539 + 15.38461539 = 0.00000000 0.00000000 + x = -11.58111774 + 15.38461539 x = -11.58111774 + 15.38461539 Combine like terms: -11.58111774 + 15.38461539 = 3.80349765 x = 3.80349765 Simplifying x = 3.80349765

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.96573313, 3.80349765}

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