-x^2+130x-2000=0

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Solution for -x^2+130x-2000=0 equation: 


Simplifying
-1x2 + 130x + -2000 = 0

Reorder the terms:
-2000 + 130x + -1x2 = 0

Solving
-2000 + 130x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2000 + -130x + x2 = 0

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + -130x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -130x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -130x + x2 = 0 + -2000
-130x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-130x + x2 = -2000

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 = -2000 + 4225

Reorder the terms:
4225 + -130x + x2 = -2000 + 4225

Combine like terms: -2000 + 4225 = 2225
4225 + -130x + x2 = 2225

Factor a perfect square on the left side:
(x + -65)(x + -65) = 2225

Calculate the square root of the right side: 47.16990566

Break this problem into two subproblems by setting 
(x + -65) equal to 47.16990566 and -47.16990566.


Subproblem 1
x + -65 = 47.16990566

Simplifying
x + -65 = 47.16990566

Reorder the terms:
-65 + x = 47.16990566

Solving
-65 + x = 47.16990566

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 = 47.16990566 + 65

Combine like terms: -65 + 65 = 0
0 + x = 47.16990566 + 65
x = 47.16990566 + 65

Combine like terms: 47.16990566 + 65 = 112.16990566
x = 112.16990566

Simplifying
x = 112.16990566


Subproblem 2
x + -65 = -47.16990566

Simplifying
x + -65 = -47.16990566

Reorder the terms:
-65 + x = -47.16990566

Solving
-65 + x = -47.16990566

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 = -47.16990566 + 65

Combine like terms: -65 + 65 = 0
0 + x = -47.16990566 + 65
x = -47.16990566 + 65

Combine like terms: -47.16990566 + 65 = 17.83009434
x = 17.83009434

Simplifying
x = 17.83009434


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {112.16990566, 17.83009434}

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