x^2-36x+108=0

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Solution for x^2-36x+108=0 equation:


Simplifying
x2 + -36x + 108 = 0

Reorder the terms:
108 + -36x + x2 = 0

Solving
108 + -36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-108' to each side of the equation.
108 + -36x + -108 + x2 = 0 + -108

Reorder the terms:
108 + -108 + -36x + x2 = 0 + -108

Combine like terms: 108 + -108 = 0
0 + -36x + x2 = 0 + -108
-36x + x2 = 0 + -108

Combine like terms: 0 + -108 = -108
-36x + x2 = -108

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -108 + 324

Reorder the terms:
324 + -36x + x2 = -108 + 324

Combine like terms: -108 + 324 = 216
324 + -36x + x2 = 216

Factor a perfect square on the left side:
(x + -18)(x + -18) = 216

Calculate the square root of the right side: 14.696938457

Break this problem into two subproblems by setting 
(x + -18) equal to 14.696938457 and -14.696938457.

Subproblem 1

x + -18 = 14.696938457 Simplifying x + -18 = 14.696938457 Reorder the terms: -18 + x = 14.696938457 Solving -18 + x = 14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 14.696938457 + 18 Combine like terms: -18 + 18 = 0 0 + x = 14.696938457 + 18 x = 14.696938457 + 18 Combine like terms: 14.696938457 + 18 = 32.696938457 x = 32.696938457 Simplifying x = 32.696938457

Subproblem 2

x + -18 = -14.696938457 Simplifying x + -18 = -14.696938457 Reorder the terms: -18 + x = -14.696938457 Solving -18 + x = -14.696938457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -14.696938457 + 18 Combine like terms: -18 + 18 = 0 0 + x = -14.696938457 + 18 x = -14.696938457 + 18 Combine like terms: -14.696938457 + 18 = 3.303061543 x = 3.303061543 Simplifying x = 3.303061543

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.696938457, 3.303061543}

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