x^2-520+3x=0

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Solution for x^2-520+3x=0 equation: 


Simplifying
x2 + -520 + 3x = 0

Reorder the terms:
-520 + 3x + x2 = 0

Solving
-520 + 3x + 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 + 3x + 520 + x2 = 0 + 520

Reorder the terms:
-520 + 520 + 3x + x2 = 0 + 520

Combine like terms: -520 + 520 = 0
0 + 3x + x2 = 0 + 520
3x + x2 = 0 + 520

Combine like terms: 0 + 520 = 520
3x + x2 = 520

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 520 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 520 + 2.25

Combine like terms: 520 + 2.25 = 522.25
2.25 + 3x + x2 = 522.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 522.25

Calculate the square root of the right side: 22.852789764

Break this problem into two subproblems by setting 
(x + 1.5) equal to 22.852789764 and -22.852789764.


Subproblem 1
x + 1.5 = 22.852789764

Simplifying
x + 1.5 = 22.852789764

Reorder the terms:
1.5 + x = 22.852789764

Solving
1.5 + x = 22.852789764

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 22.852789764 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 22.852789764 + -1.5
x = 22.852789764 + -1.5

Combine like terms: 22.852789764 + -1.5 = 21.352789764
x = 21.352789764

Simplifying
x = 21.352789764


Subproblem 2
x + 1.5 = -22.852789764

Simplifying
x + 1.5 = -22.852789764

Reorder the terms:
1.5 + x = -22.852789764

Solving
1.5 + x = -22.852789764

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -22.852789764 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -22.852789764 + -1.5
x = -22.852789764 + -1.5

Combine like terms: -22.852789764 + -1.5 = -24.352789764
x = -24.352789764

Simplifying
x = -24.352789764


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.352789764, -24.352789764}

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