x^2+(x+5)(x+5)=225

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Solution for x^2+(x+5)(x+5)=225 equation: 


Simplifying
x2 + (x + 5)(x + 5) = 225

Reorder the terms:
x2 + (5 + x)(x + 5) = 225

Reorder the terms:
x2 + (5 + x)(5 + x) = 225

Multiply (5 + x) * (5 + x)
x2 + (5(5 + x) + x(5 + x)) = 225
x2 + ((5 * 5 + x * 5) + x(5 + x)) = 225
x2 + ((25 + 5x) + x(5 + x)) = 225
x2 + (25 + 5x + (5 * x + x * x)) = 225
x2 + (25 + 5x + (5x + x2)) = 225

Combine like terms: 5x + 5x = 10x
x2 + (25 + 10x + x2) = 225

Reorder the terms:
25 + 10x + x2 + x2 = 225

Combine like terms: x2 + x2 = 2x2
25 + 10x + 2x2 = 225

Solving
25 + 10x + 2x2 = 225

Solving for variable 'x'.

Reorder the terms:
25 + -225 + 10x + 2x2 = 225 + -225

Combine like terms: 25 + -225 = -200
-200 + 10x + 2x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-200 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + 5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-100 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + 5x + x2 = 0

Solving
-100 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 5x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 5x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 5x + x2 = 0 + 100
5x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
5x + x2 = 100

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 = 100 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 100 + 6.25

Combine like terms: 100 + 6.25 = 106.25
6.25 + 5x + x2 = 106.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 106.25

Calculate the square root of the right side: 10.307764064

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.307764064 and -10.307764064.


Subproblem 1
x + 2.5 = 10.307764064

Simplifying
x + 2.5 = 10.307764064

Reorder the terms:
2.5 + x = 10.307764064

Solving
2.5 + x = 10.307764064

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 = 10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 10.307764064 + -2.5
x = 10.307764064 + -2.5

Combine like terms: 10.307764064 + -2.5 = 7.807764064
x = 7.807764064

Simplifying
x = 7.807764064


Subproblem 2
x + 2.5 = -10.307764064

Simplifying
x + 2.5 = -10.307764064

Reorder the terms:
2.5 + x = -10.307764064

Solving
2.5 + x = -10.307764064

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 = -10.307764064 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -10.307764064 + -2.5
x = -10.307764064 + -2.5

Combine like terms: -10.307764064 + -2.5 = -12.807764064
x = -12.807764064

Simplifying
x = -12.807764064


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.807764064, -12.807764064}
Solution
x = {7.807764064, -12.807764064}

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