x*(x+25)=2*(x+10)

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Solution for x*(x+25)=2*(x+10) equation: 


Simplifying
x(x + 25) = 2(x + 10)

Reorder the terms:
x(25 + x) = 2(x + 10)
(25 * x + x * x) = 2(x + 10)
(25x + x2) = 2(x + 10)

Reorder the terms:
25x + x2 = 2(10 + x)
25x + x2 = (10 * 2 + x * 2)
25x + x2 = (20 + 2x)

Solving
25x + x2 = 20 + 2x

Solving for variable 'x'.

Reorder the terms:
-20 + 25x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: 25x + -2x = 23x
-20 + 23x + x2 = 20 + 2x + -20 + -2x

Reorder the terms:
-20 + 23x + x2 = 20 + -20 + 2x + -2x

Combine like terms: 20 + -20 = 0
-20 + 23x + x2 = 0 + 2x + -2x
-20 + 23x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + 23x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 23x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 23x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 23x + x2 = 0 + 20
23x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
23x + x2 = 20

The x term is 23x.  Take half its coefficient (11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
23x + 132.25 + x2 = 20 + 132.25

Reorder the terms:
132.25 + 23x + x2 = 20 + 132.25

Combine like terms: 20 + 132.25 = 152.25
132.25 + 23x + x2 = 152.25

Factor a perfect square on the left side:
(x + 11.5)(x + 11.5) = 152.25

Calculate the square root of the right side: 12.338962679

Break this problem into two subproblems by setting 
(x + 11.5) equal to 12.338962679 and -12.338962679.


Subproblem 1
x + 11.5 = 12.338962679

Simplifying
x + 11.5 = 12.338962679

Reorder the terms:
11.5 + x = 12.338962679

Solving
11.5 + x = 12.338962679

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = 12.338962679 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = 12.338962679 + -11.5
x = 12.338962679 + -11.5

Combine like terms: 12.338962679 + -11.5 = 0.838962679
x = 0.838962679

Simplifying
x = 0.838962679


Subproblem 2
x + 11.5 = -12.338962679

Simplifying
x + 11.5 = -12.338962679

Reorder the terms:
11.5 + x = -12.338962679

Solving
11.5 + x = -12.338962679

Solving for variable 'x'.

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

Add '-11.5' to each side of the equation.
11.5 + -11.5 + x = -12.338962679 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + x = -12.338962679 + -11.5
x = -12.338962679 + -11.5

Combine like terms: -12.338962679 + -11.5 = -23.838962679
x = -23.838962679

Simplifying
x = -23.838962679


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.838962679, -23.838962679}

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