x^2+25x+2=0

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


Simplifying
x2 + 25x + 2 = 0

Reorder the terms:
2 + 25x + x2 = 0

Solving
2 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 25x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 25x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 25x + x2 = 0 + -2
25x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
25x + x2 = -2

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 = -2 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -2 + 156.25

Combine like terms: -2 + 156.25 = 154.25
156.25 + 25x + x2 = 154.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 154.25

Calculate the square root of the right side: 12.419742348

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.419742348 and -12.419742348.


Subproblem 1
x + 12.5 = 12.419742348

Simplifying
x + 12.5 = 12.419742348

Reorder the terms:
12.5 + x = 12.419742348

Solving
12.5 + x = 12.419742348

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 = 12.419742348 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.419742348 + -12.5
x = 12.419742348 + -12.5

Combine like terms: 12.419742348 + -12.5 = -0.080257652
x = -0.080257652

Simplifying
x = -0.080257652


Subproblem 2
x + 12.5 = -12.419742348

Simplifying
x + 12.5 = -12.419742348

Reorder the terms:
12.5 + x = -12.419742348

Solving
12.5 + x = -12.419742348

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 = -12.419742348 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.419742348 + -12.5
x = -12.419742348 + -12.5

Combine like terms: -12.419742348 + -12.5 = -24.919742348
x = -24.919742348

Simplifying
x = -24.919742348


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.080257652, -24.919742348}

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