2x^2+35x-7.1=0

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Solution for 2x^2+35x-7.1=0 equation: 


Simplifying
2x2 + 35x + -7.1 = 0

Reorder the terms:
-7.1 + 35x + 2x2 = 0

Solving
-7.1 + 35x + 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'.
-3.55 + 17.5x + x2 = 0

Move the constant term to the right:

Add '3.55' to each side of the equation.
-3.55 + 17.5x + 3.55 + x2 = 0 + 3.55

Reorder the terms:
-3.55 + 3.55 + 17.5x + x2 = 0 + 3.55

Combine like terms: -3.55 + 3.55 = 0.00
0.00 + 17.5x + x2 = 0 + 3.55
17.5x + x2 = 0 + 3.55

Combine like terms: 0 + 3.55 = 3.55
17.5x + x2 = 3.55

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = 3.55 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = 3.55 + 76.5625

Combine like terms: 3.55 + 76.5625 = 80.1125
76.5625 + 17.5x + x2 = 80.1125

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 80.1125

Calculate the square root of the right side: 8.950558642

Break this problem into two subproblems by setting 
(x + 8.75) equal to 8.950558642 and -8.950558642.


Subproblem 1
x + 8.75 = 8.950558642

Simplifying
x + 8.75 = 8.950558642

Reorder the terms:
8.75 + x = 8.950558642

Solving
8.75 + x = 8.950558642

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = 8.950558642 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 8.950558642 + -8.75
x = 8.950558642 + -8.75

Combine like terms: 8.950558642 + -8.75 = 0.200558642
x = 0.200558642

Simplifying
x = 0.200558642


Subproblem 2
x + 8.75 = -8.950558642

Simplifying
x + 8.75 = -8.950558642

Reorder the terms:
8.75 + x = -8.950558642

Solving
8.75 + x = -8.950558642

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = -8.950558642 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -8.950558642 + -8.75
x = -8.950558642 + -8.75

Combine like terms: -8.950558642 + -8.75 = -17.700558642
x = -17.700558642

Simplifying
x = -17.700558642


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.200558642, -17.700558642}

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