x^2+10x-520=0

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Solution for x^2+10x-520=0 equation: 


Simplifying
x2 + 10x + -520 = 0

Reorder the terms:
-520 + 10x + x2 = 0

Solving
-520 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '520' to each side of the equation.
-520 + 10x + 520 + x2 = 0 + 520

Reorder the terms:
-520 + 520 + 10x + x2 = 0 + 520

Combine like terms: -520 + 520 = 0
0 + 10x + x2 = 0 + 520
10x + x2 = 0 + 520

Combine like terms: 0 + 520 = 520
10x + x2 = 520

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 = 520 + 25

Reorder the terms:
25 + 10x + x2 = 520 + 25

Combine like terms: 520 + 25 = 545
25 + 10x + x2 = 545

Factor a perfect square on the left side:
(x + 5)(x + 5) = 545

Calculate the square root of the right side: 23.34523506

Break this problem into two subproblems by setting 
(x + 5) equal to 23.34523506 and -23.34523506.


Subproblem 1
x + 5 = 23.34523506

Simplifying
x + 5 = 23.34523506

Reorder the terms:
5 + x = 23.34523506

Solving
5 + x = 23.34523506

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 = 23.34523506 + -5

Combine like terms: 5 + -5 = 0
0 + x = 23.34523506 + -5
x = 23.34523506 + -5

Combine like terms: 23.34523506 + -5 = 18.34523506
x = 18.34523506

Simplifying
x = 18.34523506


Subproblem 2
x + 5 = -23.34523506

Simplifying
x + 5 = -23.34523506

Reorder the terms:
5 + x = -23.34523506

Solving
5 + x = -23.34523506

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 = -23.34523506 + -5

Combine like terms: 5 + -5 = 0
0 + x = -23.34523506 + -5
x = -23.34523506 + -5

Combine like terms: -23.34523506 + -5 = -28.34523506
x = -28.34523506

Simplifying
x = -28.34523506


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.34523506, -28.34523506}

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