x(x-2)-25=2x

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Solution for x(x-2)-25=2x equation: 


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

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

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

Solving
-25 + -2x + x2 = 2x

Solving for variable 'x'.

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

Combine like terms: -2x + -2x = -4x
-25 + -4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-25 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -4x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -4x + x2 = 0 + 25

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 25 + 4

Reorder the terms:
4 + -4x + x2 = 25 + 4

Combine like terms: 25 + 4 = 29
4 + -4x + x2 = 29

Factor a perfect square on the left side:
(x + -2)(x + -2) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -2) equal to 5.385164807 and -5.385164807.


Subproblem 1
x + -2 = 5.385164807

Simplifying
x + -2 = 5.385164807

Reorder the terms:
-2 + x = 5.385164807

Solving
-2 + x = 5.385164807

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 5.385164807 + 2

Combine like terms: -2 + 2 = 0
0 + x = 5.385164807 + 2
x = 5.385164807 + 2

Combine like terms: 5.385164807 + 2 = 7.385164807
x = 7.385164807

Simplifying
x = 7.385164807


Subproblem 2
x + -2 = -5.385164807

Simplifying
x + -2 = -5.385164807

Reorder the terms:
-2 + x = -5.385164807

Solving
-2 + x = -5.385164807

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -5.385164807 + 2

Combine like terms: -2 + 2 = 0
0 + x = -5.385164807 + 2
x = -5.385164807 + 2

Combine like terms: -5.385164807 + 2 = -3.385164807
x = -3.385164807

Simplifying
x = -3.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.385164807, -3.385164807}

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