x^2+240x+135=0

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Solution for x^2+240x+135=0 equation: 


Simplifying
x2 + 240x + 135 = 0

Reorder the terms:
135 + 240x + x2 = 0

Solving
135 + 240x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-135' to each side of the equation.
135 + 240x + -135 + x2 = 0 + -135

Reorder the terms:
135 + -135 + 240x + x2 = 0 + -135

Combine like terms: 135 + -135 = 0
0 + 240x + x2 = 0 + -135
240x + x2 = 0 + -135

Combine like terms: 0 + -135 = -135
240x + x2 = -135

The x term is 240x.  Take half its coefficient (120).
Square it (14400) and add it to both sides.

Add '14400' to each side of the equation.
240x + 14400 + x2 = -135 + 14400

Reorder the terms:
14400 + 240x + x2 = -135 + 14400

Combine like terms: -135 + 14400 = 14265
14400 + 240x + x2 = 14265

Factor a perfect square on the left side:
(x + 120)(x + 120) = 14265

Calculate the square root of the right side: 119.436175424

Break this problem into two subproblems by setting 
(x + 120) equal to 119.436175424 and -119.436175424.


Subproblem 1
x + 120 = 119.436175424

Simplifying
x + 120 = 119.436175424

Reorder the terms:
120 + x = 119.436175424

Solving
120 + x = 119.436175424

Solving for variable 'x'.

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

Add '-120' to each side of the equation.
120 + -120 + x = 119.436175424 + -120

Combine like terms: 120 + -120 = 0
0 + x = 119.436175424 + -120
x = 119.436175424 + -120

Combine like terms: 119.436175424 + -120 = -0.563824576
x = -0.563824576

Simplifying
x = -0.563824576


Subproblem 2
x + 120 = -119.436175424

Simplifying
x + 120 = -119.436175424

Reorder the terms:
120 + x = -119.436175424

Solving
120 + x = -119.436175424

Solving for variable 'x'.

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

Add '-120' to each side of the equation.
120 + -120 + x = -119.436175424 + -120

Combine like terms: 120 + -120 = 0
0 + x = -119.436175424 + -120
x = -119.436175424 + -120

Combine like terms: -119.436175424 + -120 = -239.436175424
x = -239.436175424

Simplifying
x = -239.436175424


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.563824576, -239.436175424}

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