3x^2+31x-5.0=0

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Solution for 3x^2+31x-5.0=0 equation:


Simplifying
3x2 + 31x + -5.0 = 0

Reorder the terms:
-5.0 + 31x + 3x2 = 0

Solving
-5.0 + 31x + 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'.
-1.666666667 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 10.33333333x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 10.33333333x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + 1.666666667
10.33333333x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
10.33333333x + x2 = 1.666666667

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = 1.666666667 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 1.666666667 + 26.69444443

Combine like terms: 1.666666667 + 26.69444443 = 28.361111097
26.69444443 + 10.33333333x + x2 = 28.361111097

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 28.361111097

Calculate the square root of the right side: 5.325515102

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.325515102 and -5.325515102.

Subproblem 1

x + 5.166666665 = 5.325515102 Simplifying x + 5.166666665 = 5.325515102 Reorder the terms: 5.166666665 + x = 5.325515102 Solving 5.166666665 + x = 5.325515102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = 5.325515102 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = 5.325515102 + -5.166666665 x = 5.325515102 + -5.166666665 Combine like terms: 5.325515102 + -5.166666665 = 0.158848437 x = 0.158848437 Simplifying x = 0.158848437

Subproblem 2

x + 5.166666665 = -5.325515102 Simplifying x + 5.166666665 = -5.325515102 Reorder the terms: 5.166666665 + x = -5.325515102 Solving 5.166666665 + x = -5.325515102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.166666665' to each side of the equation. 5.166666665 + -5.166666665 + x = -5.325515102 + -5.166666665 Combine like terms: 5.166666665 + -5.166666665 = 0.000000000 0.000000000 + x = -5.325515102 + -5.166666665 x = -5.325515102 + -5.166666665 Combine like terms: -5.325515102 + -5.166666665 = -10.492181767 x = -10.492181767 Simplifying x = -10.492181767

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.158848437, -10.492181767}

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