x^2+130x-1500=0

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Solution for x^2+130x-1500=0 equation: 


Simplifying
x2 + 130x + -1500 = 0

Reorder the terms:
-1500 + 130x + x2 = 0

Solving
-1500 + 130x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + 130x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + 130x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + 130x + x2 = 0 + 1500
130x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
130x + x2 = 1500

The x term is 130x.  Take half its coefficient (65).
Square it (4225) and add it to both sides.

Add '4225' to each side of the equation.
130x + 4225 + x2 = 1500 + 4225

Reorder the terms:
4225 + 130x + x2 = 1500 + 4225

Combine like terms: 1500 + 4225 = 5725
4225 + 130x + x2 = 5725

Factor a perfect square on the left side:
(x + 65)(x + 65) = 5725

Calculate the square root of the right side: 75.663729752

Break this problem into two subproblems by setting 
(x + 65) equal to 75.663729752 and -75.663729752.


Subproblem 1
x + 65 = 75.663729752

Simplifying
x + 65 = 75.663729752

Reorder the terms:
65 + x = 75.663729752

Solving
65 + x = 75.663729752

Solving for variable 'x'.

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

Add '-65' to each side of the equation.
65 + -65 + x = 75.663729752 + -65

Combine like terms: 65 + -65 = 0
0 + x = 75.663729752 + -65
x = 75.663729752 + -65

Combine like terms: 75.663729752 + -65 = 10.663729752
x = 10.663729752

Simplifying
x = 10.663729752


Subproblem 2
x + 65 = -75.663729752

Simplifying
x + 65 = -75.663729752

Reorder the terms:
65 + x = -75.663729752

Solving
65 + x = -75.663729752

Solving for variable 'x'.

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

Add '-65' to each side of the equation.
65 + -65 + x = -75.663729752 + -65

Combine like terms: 65 + -65 = 0
0 + x = -75.663729752 + -65
x = -75.663729752 + -65

Combine like terms: -75.663729752 + -65 = -140.663729752
x = -140.663729752

Simplifying
x = -140.663729752


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.663729752, -140.663729752}

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