x^2-6x+x^2+10x-25=x^2-16x+59

Solution for x^2-6x+x^2+10x-25=x^2-16x+59 equation:

Simplifying
x2 + -6x + x2 + 10x + -25 = x2 + -16x + 59

Reorder the terms:
-25 + -6x + 10x + x2 + x2 = x2 + -16x + 59

Combine like terms: -6x + 10x = 4x
-25 + 4x + x2 + x2 = x2 + -16x + 59

Combine like terms: x2 + x2 = 2x2
-25 + 4x + 2x2 = x2 + -16x + 59

Reorder the terms:
-25 + 4x + 2x2 = 59 + -16x + x2

Solving
-25 + 4x + 2x2 = 59 + -16x + x2

Solving for variable 'x'.

Reorder the terms:
-25 + -59 + 4x + 16x + 2x2 + -1x2 = 59 + -16x + x2 + -59 + 16x + -1x2

Combine like terms: -25 + -59 = -84
-84 + 4x + 16x + 2x2 + -1x2 = 59 + -16x + x2 + -59 + 16x + -1x2

Combine like terms: 4x + 16x = 20x
-84 + 20x + 2x2 + -1x2 = 59 + -16x + x2 + -59 + 16x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-84 + 20x + 1x2 = 59 + -16x + x2 + -59 + 16x + -1x2

Reorder the terms:
-84 + 20x + 1x2 = 59 + -59 + -16x + 16x + x2 + -1x2

Combine like terms: 59 + -59 = 0
-84 + 20x + 1x2 = 0 + -16x + 16x + x2 + -1x2
-84 + 20x + 1x2 = -16x + 16x + x2 + -1x2

Combine like terms: -16x + 16x = 0
-84 + 20x + 1x2 = 0 + x2 + -1x2
-84 + 20x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-84 + 20x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 20x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 20x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 20x + x2 = 0 + 84
20x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
20x + x2 = 84

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 84 + 100

Reorder the terms:
100 + 20x + x2 = 84 + 100

Combine like terms: 84 + 100 = 184
100 + 20x + x2 = 184

Factor a perfect square on the left side:
(x + 10)(x + 10) = 184

Calculate the square root of the right side: 13.564659966

Break this problem into two subproblems by setting 
(x + 10) equal to 13.564659966 and -13.564659966.

Subproblem 1
x + 10 = 13.564659966

Simplifying
x + 10 = 13.564659966

Reorder the terms:
10 + x = 13.564659966

Solving
10 + x = 13.564659966

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 13.564659966 + -10

Combine like terms: 10 + -10 = 0
0 + x = 13.564659966 + -10
x = 13.564659966 + -10

Combine like terms: 13.564659966 + -10 = 3.564659966
x = 3.564659966

Simplifying
x = 3.564659966

Subproblem 2
x + 10 = -13.564659966

Simplifying
x + 10 = -13.564659966

Reorder the terms:
10 + x = -13.564659966

Solving
10 + x = -13.564659966

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -13.564659966 + -10

Combine like terms: 10 + -10 = 0
0 + x = -13.564659966 + -10
x = -13.564659966 + -10

Combine like terms: -13.564659966 + -10 = -23.564659966
x = -23.564659966

Simplifying
x = -23.564659966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.564659966, -23.564659966}