x^2-13=12x-1

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Solution for x^2-13=12x-1 equation:


Simplifying
x2 + -13 = 12x + -1

Reorder the terms:
-13 + x2 = 12x + -1

Reorder the terms:
-13 + x2 = -1 + 12x

Solving
-13 + x2 = -1 + 12x

Solving for variable 'x'.

Reorder the terms:
-13 + 1 + -12x + x2 = -1 + 12x + 1 + -12x

Combine like terms: -13 + 1 = -12
-12 + -12x + x2 = -1 + 12x + 1 + -12x

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

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 12 + 36

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

Combine like terms: 12 + 36 = 48
36 + -12x + x2 = 48

Factor a perfect square on the left side:
(x + -6)(x + -6) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + -6) equal to 6.92820323 and -6.92820323.

Subproblem 1

x + -6 = 6.92820323 Simplifying x + -6 = 6.92820323 Reorder the terms: -6 + x = 6.92820323 Solving -6 + x = 6.92820323 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 = 6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.92820323 + 6 x = 6.92820323 + 6 Combine like terms: 6.92820323 + 6 = 12.92820323 x = 12.92820323 Simplifying x = 12.92820323

Subproblem 2

x + -6 = -6.92820323 Simplifying x + -6 = -6.92820323 Reorder the terms: -6 + x = -6.92820323 Solving -6 + x = -6.92820323 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 = -6.92820323 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.92820323 + 6 x = -6.92820323 + 6 Combine like terms: -6.92820323 + 6 = -0.92820323 x = -0.92820323 Simplifying x = -0.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.92820323, -0.92820323}

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