3x^2+2x-30=0

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Solution for 3x^2+2x-30=0 equation: 


Simplifying
3x2 + 2x + -30 = 0

Reorder the terms:
-30 + 2x + 3x2 = 0

Solving
-30 + 2x + 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'.
-10 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 0.6666666667x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 0.6666666667x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 0.6666666667x + x2 = 0 + 10
0.6666666667x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
0.6666666667x + x2 = 10

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 10 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 10 + 0.1111111112

Combine like terms: 10 + 0.1111111112 = 10.1111111112
0.1111111112 + 0.6666666667x + x2 = 10.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 10.1111111112

Calculate the square root of the right side: 3.179797338

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.179797338 and -3.179797338.


Subproblem 1
x + 0.3333333334 = 3.179797338

Simplifying
x + 0.3333333334 = 3.179797338

Reorder the terms:
0.3333333334 + x = 3.179797338

Solving
0.3333333334 + x = 3.179797338

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 3.179797338 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 3.179797338 + -0.3333333334
x = 3.179797338 + -0.3333333334

Combine like terms: 3.179797338 + -0.3333333334 = 2.8464640046
x = 2.8464640046

Simplifying
x = 2.8464640046


Subproblem 2
x + 0.3333333334 = -3.179797338

Simplifying
x + 0.3333333334 = -3.179797338

Reorder the terms:
0.3333333334 + x = -3.179797338

Solving
0.3333333334 + x = -3.179797338

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -3.179797338 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -3.179797338 + -0.3333333334
x = -3.179797338 + -0.3333333334

Combine like terms: -3.179797338 + -0.3333333334 = -3.5131306714
x = -3.5131306714

Simplifying
x = -3.5131306714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8464640046, -3.5131306714}

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