11x=-12x^2+20

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Solution for 11x=-12x^2+20 equation:


Simplifying
11x = -12x2 + 20

Reorder the terms:
11x = 20 + -12x2

Solving
11x = 20 + -12x2

Solving for variable 'x'.

Reorder the terms:
-20 + 11x + 12x2 = 20 + -12x2 + -20 + 12x2

Reorder the terms:
-20 + 11x + 12x2 = 20 + -20 + -12x2 + 12x2

Combine like terms: 20 + -20 = 0
-20 + 11x + 12x2 = 0 + -12x2 + 12x2
-20 + 11x + 12x2 = -12x2 + 12x2

Combine like terms: -12x2 + 12x2 = 0
-20 + 11x + 12x2 = 0

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

Divide each side by '12'.
-1.666666667 + 0.9166666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 0.9166666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 0.9166666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 0.9166666667x + x2 = 0 + 1.666666667
0.9166666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
0.9166666667x + x2 = 1.666666667

The x term is 0.9166666667x.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667x + 0.2100694445 + x2 = 1.666666667 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667x + x2 = 1.666666667 + 0.2100694445

Combine like terms: 1.666666667 + 0.2100694445 = 1.8767361115
0.2100694445 + 0.9166666667x + x2 = 1.8767361115

Factor a perfect square on the left side:
(x + 0.4583333334)(x + 0.4583333334) = 1.8767361115

Calculate the square root of the right side: 1.369940185

Break this problem into two subproblems by setting 
(x + 0.4583333334) equal to 1.369940185 and -1.369940185.

Subproblem 1

x + 0.4583333334 = 1.369940185 Simplifying x + 0.4583333334 = 1.369940185 Reorder the terms: 0.4583333334 + x = 1.369940185 Solving 0.4583333334 + x = 1.369940185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 1.369940185 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 1.369940185 + -0.4583333334 x = 1.369940185 + -0.4583333334 Combine like terms: 1.369940185 + -0.4583333334 = 0.9116068516 x = 0.9116068516 Simplifying x = 0.9116068516

Subproblem 2

x + 0.4583333334 = -1.369940185 Simplifying x + 0.4583333334 = -1.369940185 Reorder the terms: 0.4583333334 + x = -1.369940185 Solving 0.4583333334 + x = -1.369940185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -1.369940185 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -1.369940185 + -0.4583333334 x = -1.369940185 + -0.4583333334 Combine like terms: -1.369940185 + -0.4583333334 = -1.8282735184 x = -1.8282735184 Simplifying x = -1.8282735184

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9116068516, -1.8282735184}

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