2x^2+7x-520=0

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Solution for 2x^2+7x-520=0 equation: 


Simplifying
2x2 + 7x + -520 = 0

Reorder the terms:
-520 + 7x + 2x2 = 0

Solving
-520 + 7x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-260 + 3.5x + x2 = 0

Move the constant term to the right:

Add '260' to each side of the equation.
-260 + 3.5x + 260 + x2 = 0 + 260

Reorder the terms:
-260 + 260 + 3.5x + x2 = 0 + 260

Combine like terms: -260 + 260 = 0
0 + 3.5x + x2 = 0 + 260
3.5x + x2 = 0 + 260

Combine like terms: 0 + 260 = 260
3.5x + x2 = 260

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 260 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 260 + 3.0625

Combine like terms: 260 + 3.0625 = 263.0625
3.0625 + 3.5x + x2 = 263.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 263.0625

Calculate the square root of the right side: 16.219201583

Break this problem into two subproblems by setting 
(x + 1.75) equal to 16.219201583 and -16.219201583.


Subproblem 1
x + 1.75 = 16.219201583

Simplifying
x + 1.75 = 16.219201583

Reorder the terms:
1.75 + x = 16.219201583

Solving
1.75 + x = 16.219201583

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 16.219201583 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 16.219201583 + -1.75
x = 16.219201583 + -1.75

Combine like terms: 16.219201583 + -1.75 = 14.469201583
x = 14.469201583

Simplifying
x = 14.469201583


Subproblem 2
x + 1.75 = -16.219201583

Simplifying
x + 1.75 = -16.219201583

Reorder the terms:
1.75 + x = -16.219201583

Solving
1.75 + x = -16.219201583

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -16.219201583 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -16.219201583 + -1.75
x = -16.219201583 + -1.75

Combine like terms: -16.219201583 + -1.75 = -17.969201583
x = -17.969201583

Simplifying
x = -17.969201583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.469201583, -17.969201583}

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