x^2-72x+240=0

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Solution for x^2-72x+240=0 equation:


Simplifying
x2 + -72x + 240 = 0

Reorder the terms:
240 + -72x + x2 = 0

Solving
240 + -72x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-240' to each side of the equation.
240 + -72x + -240 + x2 = 0 + -240

Reorder the terms:
240 + -240 + -72x + x2 = 0 + -240

Combine like terms: 240 + -240 = 0
0 + -72x + x2 = 0 + -240
-72x + x2 = 0 + -240

Combine like terms: 0 + -240 = -240
-72x + x2 = -240

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 = -240 + 1296

Reorder the terms:
1296 + -72x + x2 = -240 + 1296

Combine like terms: -240 + 1296 = 1056
1296 + -72x + x2 = 1056

Factor a perfect square on the left side:
(x + -36)(x + -36) = 1056

Calculate the square root of the right side: 32.496153619

Break this problem into two subproblems by setting 
(x + -36) equal to 32.496153619 and -32.496153619.

Subproblem 1

x + -36 = 32.496153619 Simplifying x + -36 = 32.496153619 Reorder the terms: -36 + x = 32.496153619 Solving -36 + x = 32.496153619 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 = 32.496153619 + 36 Combine like terms: -36 + 36 = 0 0 + x = 32.496153619 + 36 x = 32.496153619 + 36 Combine like terms: 32.496153619 + 36 = 68.496153619 x = 68.496153619 Simplifying x = 68.496153619

Subproblem 2

x + -36 = -32.496153619 Simplifying x + -36 = -32.496153619 Reorder the terms: -36 + x = -32.496153619 Solving -36 + x = -32.496153619 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 = -32.496153619 + 36 Combine like terms: -36 + 36 = 0 0 + x = -32.496153619 + 36 x = -32.496153619 + 36 Combine like terms: -32.496153619 + 36 = 3.503846381 x = 3.503846381 Simplifying x = 3.503846381

Solution

The solution to the problem is based on the solutions from the subproblems. x = {68.496153619, 3.503846381}

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