20x^2+100x+25=0

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Solution for 20x^2+100x+25=0 equation: 


Simplifying
20x2 + 100x + 25 = 0

Reorder the terms:
25 + 100x + 20x2 = 0

Solving
25 + 100x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + 20x + 4x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(5 + 20x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + 20x + 4x2 = 0

Solving
5 + 20x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1.25 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 5x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 5x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 5x + x2 = 0 + -1.25
5x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
5x + x2 = -1.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -1.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.25 + 6.25

Combine like terms: -1.25 + 6.25 = 5
6.25 + 5x + x2 = 5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.236067978 and -2.236067978.


Subproblem 1
x + 2.5 = 2.236067978

Simplifying
x + 2.5 = 2.236067978

Reorder the terms:
2.5 + x = 2.236067978

Solving
2.5 + x = 2.236067978

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.236067978 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.236067978 + -2.5
x = 2.236067978 + -2.5

Combine like terms: 2.236067978 + -2.5 = -0.263932022
x = -0.263932022

Simplifying
x = -0.263932022


Subproblem 2
x + 2.5 = -2.236067978

Simplifying
x + 2.5 = -2.236067978

Reorder the terms:
2.5 + x = -2.236067978

Solving
2.5 + x = -2.236067978

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.236067978 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.236067978 + -2.5
x = -2.236067978 + -2.5

Combine like terms: -2.236067978 + -2.5 = -4.736067978
x = -4.736067978

Simplifying
x = -4.736067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.263932022, -4.736067978}
Solution
x = {-0.263932022, -4.736067978}

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