x^2+25x+42=0

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Solution for x^2+25x+42=0 equation: 


Simplifying
x2 + 25x + 42 = 0

Reorder the terms:
42 + 25x + x2 = 0

Solving
42 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 25x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + 25x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 25x + x2 = 0 + -42
25x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
25x + x2 = -42

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -42 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -42 + 156.25

Combine like terms: -42 + 156.25 = 114.25
156.25 + 25x + x2 = 114.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 114.25

Calculate the square root of the right side: 10.688779163

Break this problem into two subproblems by setting 
(x + 12.5) equal to 10.688779163 and -10.688779163.


Subproblem 1
x + 12.5 = 10.688779163

Simplifying
x + 12.5 = 10.688779163

Reorder the terms:
12.5 + x = 10.688779163

Solving
12.5 + x = 10.688779163

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 10.688779163 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 10.688779163 + -12.5
x = 10.688779163 + -12.5

Combine like terms: 10.688779163 + -12.5 = -1.811220837
x = -1.811220837

Simplifying
x = -1.811220837


Subproblem 2
x + 12.5 = -10.688779163

Simplifying
x + 12.5 = -10.688779163

Reorder the terms:
12.5 + x = -10.688779163

Solving
12.5 + x = -10.688779163

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -10.688779163 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -10.688779163 + -12.5
x = -10.688779163 + -12.5

Combine like terms: -10.688779163 + -12.5 = -23.188779163
x = -23.188779163

Simplifying
x = -23.188779163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.811220837, -23.188779163}

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