x^2-2x-75=0

Solution for x^2-2x-75=0 equation:

Simplifying
x2 + -2x + -75 = 0

Reorder the terms:
-75 + -2x + x2 = 0

Solving
-75 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -2x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -2x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -2x + x2 = 0 + 75
-2x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-2x + x2 = 75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 75 + 1

Reorder the terms:
1 + -2x + x2 = 75 + 1

Combine like terms: 75 + 1 = 76
1 + -2x + x2 = 76

Factor a perfect square on the left side:
(x + -1)(x + -1) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -1) equal to 8.717797887 and -8.717797887.

Subproblem 1
x + -1 = 8.717797887

Simplifying
x + -1 = 8.717797887

Reorder the terms:
-1 + x = 8.717797887

Solving
-1 + x = 8.717797887

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 8.717797887 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.717797887 + 1
x = 8.717797887 + 1

Combine like terms: 8.717797887 + 1 = 9.717797887
x = 9.717797887

Simplifying
x = 9.717797887

Subproblem 2
x + -1 = -8.717797887

Simplifying
x + -1 = -8.717797887

Reorder the terms:
-1 + x = -8.717797887

Solving
-1 + x = -8.717797887

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -8.717797887 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.717797887 + 1
x = -8.717797887 + 1

Combine like terms: -8.717797887 + 1 = -7.717797887
x = -7.717797887

Simplifying
x = -7.717797887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.717797887, -7.717797887}