3x^2+35x-5.9=0

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Solution for 3x^2+35x-5.9=0 equation:


Simplifying
3x2 + 35x + -5.9 = 0

Reorder the terms:
-5.9 + 35x + 3x2 = 0

Solving
-5.9 + 35x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-1.966666667 + 11.66666667x + x2 = 0

Move the constant term to the right:

Add '1.966666667' to each side of the equation.
-1.966666667 + 11.66666667x + 1.966666667 + x2 = 0 + 1.966666667

Reorder the terms:
-1.966666667 + 1.966666667 + 11.66666667x + x2 = 0 + 1.966666667

Combine like terms: -1.966666667 + 1.966666667 = 0.000000000
0.000000000 + 11.66666667x + x2 = 0 + 1.966666667
11.66666667x + x2 = 0 + 1.966666667

Combine like terms: 0 + 1.966666667 = 1.966666667
11.66666667x + x2 = 1.966666667

The x term is 11.66666667x.  Take half its coefficient (5.833333335).
Square it (34.02777780) and add it to both sides.

Add '34.02777780' to each side of the equation.
11.66666667x + 34.02777780 + x2 = 1.966666667 + 34.02777780

Reorder the terms:
34.02777780 + 11.66666667x + x2 = 1.966666667 + 34.02777780

Combine like terms: 1.966666667 + 34.02777780 = 35.994444467
34.02777780 + 11.66666667x + x2 = 35.994444467

Factor a perfect square on the left side:
(x + 5.833333335)(x + 5.833333335) = 35.994444467

Calculate the square root of the right side: 5.999537021

Break this problem into two subproblems by setting 
(x + 5.833333335) equal to 5.999537021 and -5.999537021.

Subproblem 1

x + 5.833333335 = 5.999537021 Simplifying x + 5.833333335 = 5.999537021 Reorder the terms: 5.833333335 + x = 5.999537021 Solving 5.833333335 + x = 5.999537021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.833333335' to each side of the equation. 5.833333335 + -5.833333335 + x = 5.999537021 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = 5.999537021 + -5.833333335 x = 5.999537021 + -5.833333335 Combine like terms: 5.999537021 + -5.833333335 = 0.166203686 x = 0.166203686 Simplifying x = 0.166203686

Subproblem 2

x + 5.833333335 = -5.999537021 Simplifying x + 5.833333335 = -5.999537021 Reorder the terms: 5.833333335 + x = -5.999537021 Solving 5.833333335 + x = -5.999537021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.833333335' to each side of the equation. 5.833333335 + -5.833333335 + x = -5.999537021 + -5.833333335 Combine like terms: 5.833333335 + -5.833333335 = 0.000000000 0.000000000 + x = -5.999537021 + -5.833333335 x = -5.999537021 + -5.833333335 Combine like terms: -5.999537021 + -5.833333335 = -11.832870356 x = -11.832870356 Simplifying x = -11.832870356

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.166203686, -11.832870356}

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