2x^2+71x-6=0

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Solution for 2x^2+71x-6=0 equation: 


Simplifying
2x2 + 71x + -6 = 0

Reorder the terms:
-6 + 71x + 2x2 = 0

Solving
-6 + 71x + 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'.
-3 + 35.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 35.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 35.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 35.5x + x2 = 0 + 3
35.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
35.5x + x2 = 3

The x term is 35.5x.  Take half its coefficient (17.75).
Square it (315.0625) and add it to both sides.

Add '315.0625' to each side of the equation.
35.5x + 315.0625 + x2 = 3 + 315.0625

Reorder the terms:
315.0625 + 35.5x + x2 = 3 + 315.0625

Combine like terms: 3 + 315.0625 = 318.0625
315.0625 + 35.5x + x2 = 318.0625

Factor a perfect square on the left side:
(x + 17.75)(x + 17.75) = 318.0625

Calculate the square root of the right side: 17.834306827

Break this problem into two subproblems by setting 
(x + 17.75) equal to 17.834306827 and -17.834306827.


Subproblem 1
x + 17.75 = 17.834306827

Simplifying
x + 17.75 = 17.834306827

Reorder the terms:
17.75 + x = 17.834306827

Solving
17.75 + x = 17.834306827

Solving for variable 'x'.

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

Add '-17.75' to each side of the equation.
17.75 + -17.75 + x = 17.834306827 + -17.75

Combine like terms: 17.75 + -17.75 = 0.00
0.00 + x = 17.834306827 + -17.75
x = 17.834306827 + -17.75

Combine like terms: 17.834306827 + -17.75 = 0.084306827
x = 0.084306827

Simplifying
x = 0.084306827


Subproblem 2
x + 17.75 = -17.834306827

Simplifying
x + 17.75 = -17.834306827

Reorder the terms:
17.75 + x = -17.834306827

Solving
17.75 + x = -17.834306827

Solving for variable 'x'.

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

Add '-17.75' to each side of the equation.
17.75 + -17.75 + x = -17.834306827 + -17.75

Combine like terms: 17.75 + -17.75 = 0.00
0.00 + x = -17.834306827 + -17.75
x = -17.834306827 + -17.75

Combine like terms: -17.834306827 + -17.75 = -35.584306827
x = -35.584306827

Simplifying
x = -35.584306827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.084306827, -35.584306827}

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