3x^2-111-30x=0

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Solution for 3x^2-111-30x=0 equation: 


Simplifying
3x2 + -111 + -30x = 0

Reorder the terms:
-111 + -30x + 3x2 = 0

Solving
-111 + -30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-37 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-37 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-37 + -10x + x2 = 0

Solving
-37 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + -10x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + -10x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -10x + x2 = 0 + 37
-10x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
-10x + x2 = 37

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 37 + 25

Reorder the terms:
25 + -10x + x2 = 37 + 25

Combine like terms: 37 + 25 = 62
25 + -10x + x2 = 62

Factor a perfect square on the left side:
(x + -5)(x + -5) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(x + -5) equal to 7.874007874 and -7.874007874.


Subproblem 1
x + -5 = 7.874007874

Simplifying
x + -5 = 7.874007874

Reorder the terms:
-5 + x = 7.874007874

Solving
-5 + x = 7.874007874

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 7.874007874 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.874007874 + 5
x = 7.874007874 + 5

Combine like terms: 7.874007874 + 5 = 12.874007874
x = 12.874007874

Simplifying
x = 12.874007874


Subproblem 2
x + -5 = -7.874007874

Simplifying
x + -5 = -7.874007874

Reorder the terms:
-5 + x = -7.874007874

Solving
-5 + x = -7.874007874

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -7.874007874 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.874007874 + 5
x = -7.874007874 + 5

Combine like terms: -7.874007874 + 5 = -2.874007874
x = -2.874007874

Simplifying
x = -2.874007874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.874007874, -2.874007874}
Solution
x = {12.874007874, -2.874007874}

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