x^2-60+2x=0

Solution for x^2-60+2x=0 equation:

Simplifying
x2 + -60 + 2x = 0

Reorder the terms:
-60 + 2x + x2 = 0

Solving
-60 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 2x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 2x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 2x + x2 = 0 + 60
2x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
2x + x2 = 60

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 = 60 + 1

Reorder the terms:
1 + 2x + x2 = 60 + 1

Combine like terms: 60 + 1 = 61
1 + 2x + x2 = 61

Factor a perfect square on the left side:
(x + 1)(x + 1) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(x + 1) equal to 7.810249676 and -7.810249676.

Subproblem 1
x + 1 = 7.810249676

Simplifying
x + 1 = 7.810249676

Reorder the terms:
1 + x = 7.810249676

Solving
1 + x = 7.810249676

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 = 7.810249676 + -1

Combine like terms: 1 + -1 = 0
0 + x = 7.810249676 + -1
x = 7.810249676 + -1

Combine like terms: 7.810249676 + -1 = 6.810249676
x = 6.810249676

Simplifying
x = 6.810249676

Subproblem 2
x + 1 = -7.810249676

Simplifying
x + 1 = -7.810249676

Reorder the terms:
1 + x = -7.810249676

Solving
1 + x = -7.810249676

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 = -7.810249676 + -1

Combine like terms: 1 + -1 = 0
0 + x = -7.810249676 + -1
x = -7.810249676 + -1

Combine like terms: -7.810249676 + -1 = -8.810249676
x = -8.810249676

Simplifying
x = -8.810249676

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.810249676, -8.810249676}