3x^2-30x-89=0

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Solution for 3x^2-30x-89=0 equation: 


Simplifying
3x2 + -30x + -89 = 0

Reorder the terms:
-89 + -30x + 3x2 = 0

Solving
-89 + -30x + 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'.
-29.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '29.66666667' to each side of the equation.
-29.66666667 + -10x + 29.66666667 + x2 = 0 + 29.66666667

Reorder the terms:
-29.66666667 + 29.66666667 + -10x + x2 = 0 + 29.66666667

Combine like terms: -29.66666667 + 29.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + 29.66666667
-10x + x2 = 0 + 29.66666667

Combine like terms: 0 + 29.66666667 = 29.66666667
-10x + x2 = 29.66666667

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 = 29.66666667 + 25

Reorder the terms:
25 + -10x + x2 = 29.66666667 + 25

Combine like terms: 29.66666667 + 25 = 54.66666667
25 + -10x + x2 = 54.66666667

Factor a perfect square on the left side:
(x + -5)(x + -5) = 54.66666667

Calculate the square root of the right side: 7.393691004

Break this problem into two subproblems by setting 
(x + -5) equal to 7.393691004 and -7.393691004.


Subproblem 1
x + -5 = 7.393691004

Simplifying
x + -5 = 7.393691004

Reorder the terms:
-5 + x = 7.393691004

Solving
-5 + x = 7.393691004

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 = 7.393691004 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.393691004 + 5
x = 7.393691004 + 5

Combine like terms: 7.393691004 + 5 = 12.393691004
x = 12.393691004

Simplifying
x = 12.393691004


Subproblem 2
x + -5 = -7.393691004

Simplifying
x + -5 = -7.393691004

Reorder the terms:
-5 + x = -7.393691004

Solving
-5 + x = -7.393691004

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 = -7.393691004 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.393691004 + 5
x = -7.393691004 + 5

Combine like terms: -7.393691004 + 5 = -2.393691004
x = -2.393691004

Simplifying
x = -2.393691004


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.393691004, -2.393691004}

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