30x^2-3x-12=0

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Solution for 30x^2-3x-12=0 equation: 


Simplifying
30x2 + -3x + -12 = 0

Reorder the terms:
-12 + -3x + 30x2 = 0

Solving
-12 + -3x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -1x + 10x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -1x + 10x2)' equal to zero and attempt to solve:

Simplifying
-4 + -1x + 10x2 = 0

Solving
-4 + -1x + 10x2 = 0

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

Divide each side by '10'.
-0.4 + -0.1x + x2 = 0.0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -0.1x + 0.4 + x2 = 0.0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -0.1x + x2 = 0.0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -0.1x + x2 = 0.0 + 0.4
-0.1x + x2 = 0.0 + 0.4

Combine like terms: 0.0 + 0.4 = 0.4
-0.1x + x2 = 0.4

The x term is -0.1x.  Take half its coefficient (-0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
-0.1x + 0.0025 + x2 = 0.4 + 0.0025

Reorder the terms:
0.0025 + -0.1x + x2 = 0.4 + 0.0025

Combine like terms: 0.4 + 0.0025 = 0.4025
0.0025 + -0.1x + x2 = 0.4025

Factor a perfect square on the left side:
(x + -0.05)(x + -0.05) = 0.4025

Calculate the square root of the right side: 0.634428877

Break this problem into two subproblems by setting 
(x + -0.05) equal to 0.634428877 and -0.634428877.


Subproblem 1
x + -0.05 = 0.634428877

Simplifying
x + -0.05 = 0.634428877

Reorder the terms:
-0.05 + x = 0.634428877

Solving
-0.05 + x = 0.634428877

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = 0.634428877 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = 0.634428877 + 0.05
x = 0.634428877 + 0.05

Combine like terms: 0.634428877 + 0.05 = 0.684428877
x = 0.684428877

Simplifying
x = 0.684428877


Subproblem 2
x + -0.05 = -0.634428877

Simplifying
x + -0.05 = -0.634428877

Reorder the terms:
-0.05 + x = -0.634428877

Solving
-0.05 + x = -0.634428877

Solving for variable 'x'.

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

Add '0.05' to each side of the equation.
-0.05 + 0.05 + x = -0.634428877 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + x = -0.634428877 + 0.05
x = -0.634428877 + 0.05

Combine like terms: -0.634428877 + 0.05 = -0.584428877
x = -0.584428877

Simplifying
x = -0.584428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.684428877, -0.584428877}
Solution
x = {0.684428877, -0.584428877}

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