12-x-12(x*x)=0

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Solution for 12-x-12(x*x)=0 equation:


Simplifying
12 + -1x + -12(x * x) = 0

Multiply x * x
12 + -1x + -12(x2) = 0

Solving
12 + -1x + -12x2 = 0

Solving for variable 'x'.

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

Divide each side by '-12'.
-1 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.08333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.08333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.08333333333x + x2 = 0 + 1
0.08333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.08333333333x + x2 = 1

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 = 1 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333x + x2 = 1 + 0.001736111111

Combine like terms: 1 + 0.001736111111 = 1.001736111111
0.001736111111 + 0.08333333333x + x2 = 1.001736111111

Factor a perfect square on the left side:
(x + 0.04166666667)(x + 0.04166666667) = 1.001736111111

Calculate the square root of the right side: 1.000867679

Break this problem into two subproblems by setting 
(x + 0.04166666667) equal to 1.000867679 and -1.000867679.

Subproblem 1

x + 0.04166666667 = 1.000867679 Simplifying x + 0.04166666667 = 1.000867679 Reorder the terms: 0.04166666667 + x = 1.000867679 Solving 0.04166666667 + x = 1.000867679 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 = 1.000867679 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 1.000867679 + -0.04166666667 x = 1.000867679 + -0.04166666667 Combine like terms: 1.000867679 + -0.04166666667 = 0.95920101233 x = 0.95920101233 Simplifying x = 0.95920101233

Subproblem 2

x + 0.04166666667 = -1.000867679 Simplifying x + 0.04166666667 = -1.000867679 Reorder the terms: 0.04166666667 + x = -1.000867679 Solving 0.04166666667 + x = -1.000867679 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 = -1.000867679 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -1.000867679 + -0.04166666667 x = -1.000867679 + -0.04166666667 Combine like terms: -1.000867679 + -0.04166666667 = -1.04253434567 x = -1.04253434567 Simplifying x = -1.04253434567

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.95920101233, -1.04253434567}

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