x^2+42x+135=0

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Solution for x^2+42x+135=0 equation: 


Simplifying
x2 + 42x + 135 = 0

Reorder the terms:
135 + 42x + x2 = 0

Solving
135 + 42x + 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 + 42x + -135 + x2 = 0 + -135

Reorder the terms:
135 + -135 + 42x + x2 = 0 + -135

Combine like terms: 135 + -135 = 0
0 + 42x + x2 = 0 + -135
42x + x2 = 0 + -135

Combine like terms: 0 + -135 = -135
42x + x2 = -135

The x term is 42x.  Take half its coefficient (21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
42x + 441 + x2 = -135 + 441

Reorder the terms:
441 + 42x + x2 = -135 + 441

Combine like terms: -135 + 441 = 306
441 + 42x + x2 = 306

Factor a perfect square on the left side:
(x + 21)(x + 21) = 306

Calculate the square root of the right side: 17.492855685

Break this problem into two subproblems by setting 
(x + 21) equal to 17.492855685 and -17.492855685.


Subproblem 1
x + 21 = 17.492855685

Simplifying
x + 21 = 17.492855685

Reorder the terms:
21 + x = 17.492855685

Solving
21 + x = 17.492855685

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = 17.492855685 + -21

Combine like terms: 21 + -21 = 0
0 + x = 17.492855685 + -21
x = 17.492855685 + -21

Combine like terms: 17.492855685 + -21 = -3.507144315
x = -3.507144315

Simplifying
x = -3.507144315


Subproblem 2
x + 21 = -17.492855685

Simplifying
x + 21 = -17.492855685

Reorder the terms:
21 + x = -17.492855685

Solving
21 + x = -17.492855685

Solving for variable 'x'.

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

Add '-21' to each side of the equation.
21 + -21 + x = -17.492855685 + -21

Combine like terms: 21 + -21 = 0
0 + x = -17.492855685 + -21
x = -17.492855685 + -21

Combine like terms: -17.492855685 + -21 = -38.492855685
x = -38.492855685

Simplifying
x = -38.492855685


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.507144315, -38.492855685}

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