2x^2+35x-5.9=0

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Solution for 2x^2+35x-5.9=0 equation: 


Simplifying
2x2 + 35x + -5.9 = 0

Reorder the terms:
-5.9 + 35x + 2x2 = 0

Solving
-5.9 + 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'.
-2.95 + 17.5x + x2 = 0

Move the constant term to the right:

Add '2.95' to each side of the equation.
-2.95 + 17.5x + 2.95 + x2 = 0 + 2.95

Reorder the terms:
-2.95 + 2.95 + 17.5x + x2 = 0 + 2.95

Combine like terms: -2.95 + 2.95 = 0.00
0.00 + 17.5x + x2 = 0 + 2.95
17.5x + x2 = 0 + 2.95

Combine like terms: 0 + 2.95 = 2.95
17.5x + x2 = 2.95

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 = 2.95 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = 2.95 + 76.5625

Combine like terms: 2.95 + 76.5625 = 79.5125
76.5625 + 17.5x + x2 = 79.5125

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 79.5125

Calculate the square root of the right side: 8.916978188

Break this problem into two subproblems by setting 
(x + 8.75) equal to 8.916978188 and -8.916978188.


Subproblem 1
x + 8.75 = 8.916978188

Simplifying
x + 8.75 = 8.916978188

Reorder the terms:
8.75 + x = 8.916978188

Solving
8.75 + x = 8.916978188

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 = 8.916978188 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 8.916978188 + -8.75
x = 8.916978188 + -8.75

Combine like terms: 8.916978188 + -8.75 = 0.166978188
x = 0.166978188

Simplifying
x = 0.166978188


Subproblem 2
x + 8.75 = -8.916978188

Simplifying
x + 8.75 = -8.916978188

Reorder the terms:
8.75 + x = -8.916978188

Solving
8.75 + x = -8.916978188

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 = -8.916978188 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -8.916978188 + -8.75
x = -8.916978188 + -8.75

Combine like terms: -8.916978188 + -8.75 = -17.666978188
x = -17.666978188

Simplifying
x = -17.666978188


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.166978188, -17.666978188}

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