6.28x^2+81.64x-716=0

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Solution for 6.28x^2+81.64x-716=0 equation: 


Simplifying
6.28x2 + 81.64x + -716 = 0

Reorder the terms:
-716 + 81.64x + 6.28x2 = 0

Solving
-716 + 81.64x + 6.28x2 = 0

Solving for variable 'x'.

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

Divide each side by '6.28'.
-114.0127389 + 13x + x2 = 0

Move the constant term to the right:

Add '114.0127389' to each side of the equation.
-114.0127389 + 13x + 114.0127389 + x2 = 0 + 114.0127389

Reorder the terms:
-114.0127389 + 114.0127389 + 13x + x2 = 0 + 114.0127389

Combine like terms: -114.0127389 + 114.0127389 = 0.0000000
0.0000000 + 13x + x2 = 0 + 114.0127389
13x + x2 = 0 + 114.0127389

Combine like terms: 0 + 114.0127389 = 114.0127389
13x + x2 = 114.0127389

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 114.0127389 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 114.0127389 + 42.25

Combine like terms: 114.0127389 + 42.25 = 156.2627389
42.25 + 13x + x2 = 156.2627389

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 156.2627389

Calculate the square root of the right side: 12.500509546

Break this problem into two subproblems by setting 
(x + 6.5) equal to 12.500509546 and -12.500509546.


Subproblem 1
x + 6.5 = 12.500509546

Simplifying
x + 6.5 = 12.500509546

Reorder the terms:
6.5 + x = 12.500509546

Solving
6.5 + x = 12.500509546

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 12.500509546 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 12.500509546 + -6.5
x = 12.500509546 + -6.5

Combine like terms: 12.500509546 + -6.5 = 6.000509546
x = 6.000509546

Simplifying
x = 6.000509546


Subproblem 2
x + 6.5 = -12.500509546

Simplifying
x + 6.5 = -12.500509546

Reorder the terms:
6.5 + x = -12.500509546

Solving
6.5 + x = -12.500509546

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -12.500509546 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -12.500509546 + -6.5
x = -12.500509546 + -6.5

Combine like terms: -12.500509546 + -6.5 = -19.000509546
x = -19.000509546

Simplifying
x = -19.000509546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.000509546, -19.000509546}

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