x=12x^2-56x+56

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Solution for x=12x^2-56x+56 equation:


Simplifying
x = 12x2 + -56x + 56

Reorder the terms:
x = 56 + -56x + 12x2

Solving
x = 56 + -56x + 12x2

Solving for variable 'x'.

Reorder the terms:
-56 + x + 56x + -12x2 = 56 + -56x + 12x2 + -56 + 56x + -12x2

Combine like terms: x + 56x = 57x
-56 + 57x + -12x2 = 56 + -56x + 12x2 + -56 + 56x + -12x2

Reorder the terms:
-56 + 57x + -12x2 = 56 + -56 + -56x + 56x + 12x2 + -12x2

Combine like terms: 56 + -56 = 0
-56 + 57x + -12x2 = 0 + -56x + 56x + 12x2 + -12x2
-56 + 57x + -12x2 = -56x + 56x + 12x2 + -12x2

Combine like terms: -56x + 56x = 0
-56 + 57x + -12x2 = 0 + 12x2 + -12x2
-56 + 57x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-56 + 57x + -12x2 = 0

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

Divide each side by '-12'.
4.666666667 + -4.75x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.75x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -4.75x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -4.75x + x2 = 0 + -4.666666667
-4.75x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-4.75x + x2 = -4.666666667

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = -4.666666667 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = -4.666666667 + 5.640625

Combine like terms: -4.666666667 + 5.640625 = 0.973958333
5.640625 + -4.75x + x2 = 0.973958333

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 0.973958333

Calculate the square root of the right side: 0.986893273

Break this problem into two subproblems by setting 
(x + -2.375) equal to 0.986893273 and -0.986893273.

Subproblem 1

x + -2.375 = 0.986893273 Simplifying x + -2.375 = 0.986893273 Reorder the terms: -2.375 + x = 0.986893273 Solving -2.375 + x = 0.986893273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 0.986893273 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 0.986893273 + 2.375 x = 0.986893273 + 2.375 Combine like terms: 0.986893273 + 2.375 = 3.361893273 x = 3.361893273 Simplifying x = 3.361893273

Subproblem 2

x + -2.375 = -0.986893273 Simplifying x + -2.375 = -0.986893273 Reorder the terms: -2.375 + x = -0.986893273 Solving -2.375 + x = -0.986893273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -0.986893273 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -0.986893273 + 2.375 x = -0.986893273 + 2.375 Combine like terms: -0.986893273 + 2.375 = 1.388106727 x = 1.388106727 Simplifying x = 1.388106727

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.361893273, 1.388106727}

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