52=x^2+10x+25*(x-2)

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Solution for 52=x^2+10x+25*(x-2) equation: 


Simplifying
52 = x2 + 10x + 25(x + -2)

Reorder the terms:
52 = x2 + 10x + 25(-2 + x)
52 = x2 + 10x + (-2 * 25 + x * 25)
52 = x2 + 10x + (-50 + 25x)

Reorder the terms:
52 = -50 + 10x + 25x + x2

Combine like terms: 10x + 25x = 35x
52 = -50 + 35x + x2

Solving
52 = -50 + 35x + x2

Solving for variable 'x'.

Combine like terms: 52 + 50 = 102
102 + -35x + -1x2 = -50 + 35x + x2 + 50 + -35x + -1x2

Reorder the terms:
102 + -35x + -1x2 = -50 + 50 + 35x + -35x + x2 + -1x2

Combine like terms: -50 + 50 = 0
102 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2
102 + -35x + -1x2 = 35x + -35x + x2 + -1x2

Combine like terms: 35x + -35x = 0
102 + -35x + -1x2 = 0 + x2 + -1x2
102 + -35x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
102 + -35x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-102 + 35x + x2 = 0

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 35x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 35x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 35x + x2 = 0 + 102
35x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
35x + x2 = 102

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 102 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 102 + 306.25

Combine like terms: 102 + 306.25 = 408.25
306.25 + 35x + x2 = 408.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 408.25

Calculate the square root of the right side: 20.205197351

Break this problem into two subproblems by setting 
(x + 17.5) equal to 20.205197351 and -20.205197351.


Subproblem 1
x + 17.5 = 20.205197351

Simplifying
x + 17.5 = 20.205197351

Reorder the terms:
17.5 + x = 20.205197351

Solving
17.5 + x = 20.205197351

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 20.205197351 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 20.205197351 + -17.5
x = 20.205197351 + -17.5

Combine like terms: 20.205197351 + -17.5 = 2.705197351
x = 2.705197351

Simplifying
x = 2.705197351


Subproblem 2
x + 17.5 = -20.205197351

Simplifying
x + 17.5 = -20.205197351

Reorder the terms:
17.5 + x = -20.205197351

Solving
17.5 + x = -20.205197351

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -20.205197351 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -20.205197351 + -17.5
x = -20.205197351 + -17.5

Combine like terms: -20.205197351 + -17.5 = -37.705197351
x = -37.705197351

Simplifying
x = -37.705197351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.705197351, -37.705197351}

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