x(x+25)=126

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Solution for x(x+25)=126 equation: 


Simplifying
x(x + 25) = 126

Reorder the terms:
x(25 + x) = 126
(25 * x + x * x) = 126
(25x + x2) = 126

Solving
25x + x2 = 126

Solving for variable 'x'.

Reorder the terms:
-126 + 25x + x2 = 126 + -126

Combine like terms: 126 + -126 = 0
-126 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '126' to each side of the equation.
-126 + 25x + 126 + x2 = 0 + 126

Reorder the terms:
-126 + 126 + 25x + x2 = 0 + 126

Combine like terms: -126 + 126 = 0
0 + 25x + x2 = 0 + 126
25x + x2 = 0 + 126

Combine like terms: 0 + 126 = 126
25x + x2 = 126

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 = 126 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 126 + 156.25

Combine like terms: 126 + 156.25 = 282.25
156.25 + 25x + x2 = 282.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(x + 12.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
x + 12.5 = 16.800297616

Simplifying
x + 12.5 = 16.800297616

Reorder the terms:
12.5 + x = 16.800297616

Solving
12.5 + x = 16.800297616

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 = 16.800297616 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 16.800297616 + -12.5
x = 16.800297616 + -12.5

Combine like terms: 16.800297616 + -12.5 = 4.300297616
x = 4.300297616

Simplifying
x = 4.300297616


Subproblem 2
x + 12.5 = -16.800297616

Simplifying
x + 12.5 = -16.800297616

Reorder the terms:
12.5 + x = -16.800297616

Solving
12.5 + x = -16.800297616

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 = -16.800297616 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -16.800297616 + -12.5
x = -16.800297616 + -12.5

Combine like terms: -16.800297616 + -12.5 = -29.300297616
x = -29.300297616

Simplifying
x = -29.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.300297616, -29.300297616}

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