12x^2-26=x

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Solution for 12x^2-26=x equation:


Simplifying
12x2 + -26 = x

Reorder the terms:
-26 + 12x2 = x

Solving
-26 + 12x2 = x

Solving for variable 'x'.

Reorder the terms:
-26 + -1x + 12x2 = x + -1x

Combine like terms: x + -1x = 0
-26 + -1x + 12x2 = 0

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

Divide each side by '12'.
-2.166666667 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + -0.08333333333x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + -0.08333333333x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + -0.08333333333x + x2 = 0 + 2.166666667
-0.08333333333x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
-0.08333333333x + x2 = 2.166666667

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 2.166666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 2.166666667 + 0.001736111111

Combine like terms: 2.166666667 + 0.001736111111 = 2.168402778111
0.001736111111 + -0.08333333333x + x2 = 2.168402778111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 2.168402778111

Calculate the square root of the right side: 1.472549754

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 1.472549754 and -1.472549754.

Subproblem 1

x + -0.04166666667 = 1.472549754 Simplifying x + -0.04166666667 = 1.472549754 Reorder the terms: -0.04166666667 + x = 1.472549754 Solving -0.04166666667 + x = 1.472549754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 1.472549754 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 1.472549754 + 0.04166666667 x = 1.472549754 + 0.04166666667 Combine like terms: 1.472549754 + 0.04166666667 = 1.51421642067 x = 1.51421642067 Simplifying x = 1.51421642067

Subproblem 2

x + -0.04166666667 = -1.472549754 Simplifying x + -0.04166666667 = -1.472549754 Reorder the terms: -0.04166666667 + x = -1.472549754 Solving -0.04166666667 + x = -1.472549754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -1.472549754 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -1.472549754 + 0.04166666667 x = -1.472549754 + 0.04166666667 Combine like terms: -1.472549754 + 0.04166666667 = -1.43088308733 x = -1.43088308733 Simplifying x = -1.43088308733

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.51421642067, -1.43088308733}

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