x^2-10x+25=75

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Solution for x^2-10x+25=75 equation: 


Simplifying
x2 + -10x + 25 = 75

Reorder the terms:
25 + -10x + x2 = 75

Solving
25 + -10x + x2 = 75

Solving for variable 'x'.

Reorder the terms:
25 + -75 + -10x + x2 = 75 + -75

Combine like terms: 25 + -75 = -50
-50 + -10x + x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-50 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -10x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -10x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -10x + x2 = 0 + 50
-10x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-10x + x2 = 50

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 50 + 25

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

Combine like terms: 50 + 25 = 75
25 + -10x + x2 = 75

Factor a perfect square on the left side:
(x + -5)(x + -5) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -5) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + -5 = 8.660254038

Simplifying
x + -5 = 8.660254038

Reorder the terms:
-5 + x = 8.660254038

Solving
-5 + x = 8.660254038

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 8.660254038 + 5

Combine like terms: -5 + 5 = 0
0 + x = 8.660254038 + 5
x = 8.660254038 + 5

Combine like terms: 8.660254038 + 5 = 13.660254038
x = 13.660254038

Simplifying
x = 13.660254038


Subproblem 2
x + -5 = -8.660254038

Simplifying
x + -5 = -8.660254038

Reorder the terms:
-5 + x = -8.660254038

Solving
-5 + x = -8.660254038

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -8.660254038 + 5

Combine like terms: -5 + 5 = 0
0 + x = -8.660254038 + 5
x = -8.660254038 + 5

Combine like terms: -8.660254038 + 5 = -3.660254038
x = -3.660254038

Simplifying
x = -3.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.660254038, -3.660254038}

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