x^2-72x+72=0

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Solution for x^2-72x+72=0 equation:


Simplifying
x2 + -72x + 72 = 0

Reorder the terms:
72 + -72x + x2 = 0

Solving
72 + -72x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -72x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + -72x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -72x + x2 = 0 + -72
-72x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-72x + x2 = -72

The x term is -72x.  Take half its coefficient (-36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
-72x + 1296 + x2 = -72 + 1296

Reorder the terms:
1296 + -72x + x2 = -72 + 1296

Combine like terms: -72 + 1296 = 1224
1296 + -72x + x2 = 1224

Factor a perfect square on the left side:
(x + -36)(x + -36) = 1224

Calculate the square root of the right side: 34.985711369

Break this problem into two subproblems by setting 
(x + -36) equal to 34.985711369 and -34.985711369.

Subproblem 1

x + -36 = 34.985711369 Simplifying x + -36 = 34.985711369 Reorder the terms: -36 + x = 34.985711369 Solving -36 + x = 34.985711369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = 34.985711369 + 36 Combine like terms: -36 + 36 = 0 0 + x = 34.985711369 + 36 x = 34.985711369 + 36 Combine like terms: 34.985711369 + 36 = 70.985711369 x = 70.985711369 Simplifying x = 70.985711369

Subproblem 2

x + -36 = -34.985711369 Simplifying x + -36 = -34.985711369 Reorder the terms: -36 + x = -34.985711369 Solving -36 + x = -34.985711369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + x = -34.985711369 + 36 Combine like terms: -36 + 36 = 0 0 + x = -34.985711369 + 36 x = -34.985711369 + 36 Combine like terms: -34.985711369 + 36 = 1.014288631 x = 1.014288631 Simplifying x = 1.014288631

Solution

The solution to the problem is based on the solutions from the subproblems. x = {70.985711369, 1.014288631}

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