x^2-12x-1=-4

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Solution for x^2-12x-1=-4 equation:


Simplifying
x2 + -12x + -1 = -4

Reorder the terms:
-1 + -12x + x2 = -4

Solving
-1 + -12x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
-1 + 4 + -12x + x2 = -4 + 4

Combine like terms: -1 + 4 = 3
3 + -12x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
3 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -12x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -12x + x2 = 0 + -3
-12x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12x + x2 = -3

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -3 + 36

Reorder the terms:
36 + -12x + x2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + -12x + x2 = 33

Factor a perfect square on the left side:
(x + -6)(x + -6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -6) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -6 = 5.744562647 Simplifying x + -6 = 5.744562647 Reorder the terms: -6 + x = 5.744562647 Solving -6 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.744562647 + 6 x = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 x = 11.744562647 Simplifying x = 11.744562647

Subproblem 2

x + -6 = -5.744562647 Simplifying x + -6 = -5.744562647 Reorder the terms: -6 + x = -5.744562647 Solving -6 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.744562647 + 6 x = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 x = 0.255437353 Simplifying x = 0.255437353

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.744562647, 0.255437353}

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