0=3x^2+25x-5.9

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Solution for 0=3x^2+25x-5.9 equation:


Simplifying
0 = 3x2 + 25x + -5.9

Reorder the terms:
0 = -5.9 + 25x + 3x2

Solving
0 = -5.9 + 25x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 5.9 = 5.9
5.9 + -25x + -3x2 = -5.9 + 25x + 3x2 + 5.9 + -25x + -3x2

Reorder the terms:
5.9 + -25x + -3x2 = -5.9 + 5.9 + 25x + -25x + 3x2 + -3x2

Combine like terms: -5.9 + 5.9 = 0.0
5.9 + -25x + -3x2 = 0.0 + 25x + -25x + 3x2 + -3x2
5.9 + -25x + -3x2 = 25x + -25x + 3x2 + -3x2

Combine like terms: 25x + -25x = 0
5.9 + -25x + -3x2 = 0 + 3x2 + -3x2
5.9 + -25x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
5.9 + -25x + -3x2 = 0

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

Divide each side by '-3'.
-1.966666667 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '1.966666667' to each side of the equation.
-1.966666667 + 8.333333333x + 1.966666667 + x2 = 0 + 1.966666667

Reorder the terms:
-1.966666667 + 1.966666667 + 8.333333333x + x2 = 0 + 1.966666667

Combine like terms: -1.966666667 + 1.966666667 = 0.000000000
0.000000000 + 8.333333333x + x2 = 0 + 1.966666667
8.333333333x + x2 = 0 + 1.966666667

Combine like terms: 0 + 1.966666667 = 1.966666667
8.333333333x + x2 = 1.966666667

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 1.966666667 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 1.966666667 + 17.36111111

Combine like terms: 1.966666667 + 17.36111111 = 19.327777777
17.36111111 + 8.333333333x + x2 = 19.327777777

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 19.327777777

Calculate the square root of the right side: 4.396336859

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 4.396336859 and -4.396336859.

Subproblem 1

x + 4.166666667 = 4.396336859 Simplifying x + 4.166666667 = 4.396336859 Reorder the terms: 4.166666667 + x = 4.396336859 Solving 4.166666667 + x = 4.396336859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 4.396336859 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 4.396336859 + -4.166666667 x = 4.396336859 + -4.166666667 Combine like terms: 4.396336859 + -4.166666667 = 0.229670192 x = 0.229670192 Simplifying x = 0.229670192

Subproblem 2

x + 4.166666667 = -4.396336859 Simplifying x + 4.166666667 = -4.396336859 Reorder the terms: 4.166666667 + x = -4.396336859 Solving 4.166666667 + x = -4.396336859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -4.396336859 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -4.396336859 + -4.166666667 x = -4.396336859 + -4.166666667 Combine like terms: -4.396336859 + -4.166666667 = -8.563003526 x = -8.563003526 Simplifying x = -8.563003526

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.229670192, -8.563003526}

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