x^2+20x+25=0

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Solution for x^2+20x+25=0 equation:


Simplifying
x2 + 20x + 25 = 0

Reorder the terms:
25 + 20x + x2 = 0

Solving
25 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 20x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 20x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 20x + x2 = 0 + -25
20x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
20x + x2 = -25

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -25 + 100

Reorder the terms:
100 + 20x + x2 = -25 + 100

Combine like terms: -25 + 100 = 75
100 + 20x + x2 = 75

Factor a perfect square on the left side:
(x + 10)(x + 10) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + 10) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + 10 = 8.660254038

Simplifying
x + 10 = 8.660254038

Reorder the terms:
10 + x = 8.660254038

Solving
10 + x = 8.660254038

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 8.660254038 + -10

Combine like terms: 10 + -10 = 0
0 + x = 8.660254038 + -10
x = 8.660254038 + -10

Combine like terms: 8.660254038 + -10 = -1.339745962
x = -1.339745962

Simplifying
x = -1.339745962


Subproblem 2
x + 10 = -8.660254038

Simplifying
x + 10 = -8.660254038

Reorder the terms:
10 + x = -8.660254038

Solving
10 + x = -8.660254038

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -8.660254038 + -10

Combine like terms: 10 + -10 = 0
0 + x = -8.660254038 + -10
x = -8.660254038 + -10

Combine like terms: -8.660254038 + -10 = -18.660254038
x = -18.660254038

Simplifying
x = -18.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.339745962, -18.660254038}

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