x^2-40x-240=0

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Solution for x^2-40x-240=0 equation: 


Simplifying
x2 + -40x + -240 = 0

Reorder the terms:
-240 + -40x + x2 = 0

Solving
-240 + -40x + 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 + -40x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + -40x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + -40x + x2 = 0 + 240
-40x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
-40x + x2 = 240

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 240 + 400

Reorder the terms:
400 + -40x + x2 = 240 + 400

Combine like terms: 240 + 400 = 640
400 + -40x + x2 = 640

Factor a perfect square on the left side:
(x + -20)(x + -20) = 640

Calculate the square root of the right side: 25.298221281

Break this problem into two subproblems by setting 
(x + -20) equal to 25.298221281 and -25.298221281.


Subproblem 1
x + -20 = 25.298221281

Simplifying
x + -20 = 25.298221281

Reorder the terms:
-20 + x = 25.298221281

Solving
-20 + x = 25.298221281

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.
-20 + 20 + x = 25.298221281 + 20

Combine like terms: -20 + 20 = 0
0 + x = 25.298221281 + 20
x = 25.298221281 + 20

Combine like terms: 25.298221281 + 20 = 45.298221281
x = 45.298221281

Simplifying
x = 45.298221281


Subproblem 2
x + -20 = -25.298221281

Simplifying
x + -20 = -25.298221281

Reorder the terms:
-20 + x = -25.298221281

Solving
-20 + x = -25.298221281

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.
-20 + 20 + x = -25.298221281 + 20

Combine like terms: -20 + 20 = 0
0 + x = -25.298221281 + 20
x = -25.298221281 + 20

Combine like terms: -25.298221281 + 20 = -5.298221281
x = -5.298221281

Simplifying
x = -5.298221281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.298221281, -5.298221281}

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