3x^2-30x-56=0

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Solution for 3x^2-30x-56=0 equation: 


Simplifying
3x2 + -30x + -56 = 0

Reorder the terms:
-56 + -30x + 3x2 = 0

Solving
-56 + -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'.
-18.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -10x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -10x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + 18.66666667
-10x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-10x + x2 = 18.66666667

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 = 18.66666667 + 25

Reorder the terms:
25 + -10x + x2 = 18.66666667 + 25

Combine like terms: 18.66666667 + 25 = 43.66666667
25 + -10x + x2 = 43.66666667

Factor a perfect square on the left side:
(x + -5)(x + -5) = 43.66666667

Calculate the square root of the right side: 6.608075867

Break this problem into two subproblems by setting 
(x + -5) equal to 6.608075867 and -6.608075867.


Subproblem 1
x + -5 = 6.608075867

Simplifying
x + -5 = 6.608075867

Reorder the terms:
-5 + x = 6.608075867

Solving
-5 + x = 6.608075867

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 = 6.608075867 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.608075867 + 5
x = 6.608075867 + 5

Combine like terms: 6.608075867 + 5 = 11.608075867
x = 11.608075867

Simplifying
x = 11.608075867


Subproblem 2
x + -5 = -6.608075867

Simplifying
x + -5 = -6.608075867

Reorder the terms:
-5 + x = -6.608075867

Solving
-5 + x = -6.608075867

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 = -6.608075867 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.608075867 + 5
x = -6.608075867 + 5

Combine like terms: -6.608075867 + 5 = -1.608075867
x = -1.608075867

Simplifying
x = -1.608075867


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.608075867, -1.608075867}

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