x^2-1580x+60950=0

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Solution for x^2-1580x+60950=0 equation: 


Simplifying
x2 + -1580x + 60950 = 0

Reorder the terms:
60950 + -1580x + x2 = 0

Solving
60950 + -1580x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-60950' to each side of the equation.
60950 + -1580x + -60950 + x2 = 0 + -60950

Reorder the terms:
60950 + -60950 + -1580x + x2 = 0 + -60950

Combine like terms: 60950 + -60950 = 0
0 + -1580x + x2 = 0 + -60950
-1580x + x2 = 0 + -60950

Combine like terms: 0 + -60950 = -60950
-1580x + x2 = -60950

The x term is -1580x.  Take half its coefficient (-790).
Square it (624100) and add it to both sides.

Add '624100' to each side of the equation.
-1580x + 624100 + x2 = -60950 + 624100

Reorder the terms:
624100 + -1580x + x2 = -60950 + 624100

Combine like terms: -60950 + 624100 = 563150
624100 + -1580x + x2 = 563150

Factor a perfect square on the left side:
(x + -790)(x + -790) = 563150

Calculate the square root of the right side: 750.43320822

Break this problem into two subproblems by setting 
(x + -790) equal to 750.43320822 and -750.43320822.


Subproblem 1
x + -790 = 750.43320822

Simplifying
x + -790 = 750.43320822

Reorder the terms:
-790 + x = 750.43320822

Solving
-790 + x = 750.43320822

Solving for variable 'x'.

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

Add '790' to each side of the equation.
-790 + 790 + x = 750.43320822 + 790

Combine like terms: -790 + 790 = 0
0 + x = 750.43320822 + 790
x = 750.43320822 + 790

Combine like terms: 750.43320822 + 790 = 1540.43320822
x = 1540.43320822

Simplifying
x = 1540.43320822


Subproblem 2
x + -790 = -750.43320822

Simplifying
x + -790 = -750.43320822

Reorder the terms:
-790 + x = -750.43320822

Solving
-790 + x = -750.43320822

Solving for variable 'x'.

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

Add '790' to each side of the equation.
-790 + 790 + x = -750.43320822 + 790

Combine like terms: -790 + 790 = 0
0 + x = -750.43320822 + 790
x = -750.43320822 + 790

Combine like terms: -750.43320822 + 790 = 39.56679178
x = 39.56679178

Simplifying
x = 39.56679178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1540.43320822, 39.56679178}

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