x^2-12x+5=0

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Solution for x^2-12x+5=0 equation:


Simplifying
x2 + -12x + 5 = 0

Reorder the terms:
5 + -12x + x2 = 0

Solving
5 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -12x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -12x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -12x + x2 = 0 + -5
-12x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-12x + x2 = -5

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 = -5 + 36

Reorder the terms:
36 + -12x + x2 = -5 + 36

Combine like terms: -5 + 36 = 31
36 + -12x + x2 = 31

Factor a perfect square on the left side:
(x + -6)(x + -6) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -6) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + -6 = 5.567764363 Simplifying x + -6 = 5.567764363 Reorder the terms: -6 + x = 5.567764363 Solving -6 + x = 5.567764363 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 = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.567764363 + 6 x = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 x = 11.567764363 Simplifying x = 11.567764363

Subproblem 2

x + -6 = -5.567764363 Simplifying x + -6 = -5.567764363 Reorder the terms: -6 + x = -5.567764363 Solving -6 + x = -5.567764363 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 = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.567764363 + 6 x = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 x = 0.432235637 Simplifying x = 0.432235637

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.567764363, 0.432235637}

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