(2x)(2x)+(20x)=25

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Solution for (2x)(2x)+(20x)=25 equation: 


Simplifying
(2x)(2x) + (20x) = 25

Remove parenthesis around (2x)
2x(2x) + (20x) = 25

Remove parenthesis around (2x)
2x * 2x + (20x) = 25

Reorder the terms for easier multiplication:
2 * 2x * x + (20x) = 25

Multiply 2 * 2
4x * x + (20x) = 25

Multiply x * x
4x2 + (20x) = 25

Reorder the terms:
(20x) + 4x2 = 25

Solving
(20x) + 4x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + (20x) + 4x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + (20x) + 4x2 = 0

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

Divide each side by '4'.
-6.25 + (5x) + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + (5x) + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + (5x) + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + (5x) + x2 = 0 + 6.25
(5x) + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
(5x) + x2 = 6.25

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 = 6.25 + 6.25

Reorder the terms:
6.25 + (5x) + x2 = 6.25 + 6.25

Combine like terms: 6.25 + 6.25 = 12.5
6.25 + (5x) + x2 = 12.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.535533906 and -3.535533906.


Subproblem 1
x + 2.5 = 3.535533906

Simplifying
x + 2.5 = 3.535533906

Reorder the terms:
2.5 + x = 3.535533906

Solving
2.5 + x = 3.535533906

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 = 3.535533906 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.535533906 + -2.5
x = 3.535533906 + -2.5

Combine like terms: 3.535533906 + -2.5 = 1.035533906
x = 1.035533906

Simplifying
x = 1.035533906


Subproblem 2
x + 2.5 = -3.535533906

Simplifying
x + 2.5 = -3.535533906

Reorder the terms:
2.5 + x = -3.535533906

Solving
2.5 + x = -3.535533906

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 = -3.535533906 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.535533906 + -2.5
x = -3.535533906 + -2.5

Combine like terms: -3.535533906 + -2.5 = -6.035533906
x = -6.035533906

Simplifying
x = -6.035533906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.035533906, -6.035533906}

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