3x^2-30x-77=0

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Solution for 3x^2-30x-77=0 equation: 


Simplifying
3x2 + -30x + -77 = 0

Reorder the terms:
-77 + -30x + 3x2 = 0

Solving
-77 + -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'.
-25.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '25.66666667' to each side of the equation.
-25.66666667 + -10x + 25.66666667 + x2 = 0 + 25.66666667

Reorder the terms:
-25.66666667 + 25.66666667 + -10x + x2 = 0 + 25.66666667

Combine like terms: -25.66666667 + 25.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + 25.66666667
-10x + x2 = 0 + 25.66666667

Combine like terms: 0 + 25.66666667 = 25.66666667
-10x + x2 = 25.66666667

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 = 25.66666667 + 25

Reorder the terms:
25 + -10x + x2 = 25.66666667 + 25

Combine like terms: 25.66666667 + 25 = 50.66666667
25 + -10x + x2 = 50.66666667

Factor a perfect square on the left side:
(x + -5)(x + -5) = 50.66666667

Calculate the square root of the right side: 7.118052168

Break this problem into two subproblems by setting 
(x + -5) equal to 7.118052168 and -7.118052168.


Subproblem 1
x + -5 = 7.118052168

Simplifying
x + -5 = 7.118052168

Reorder the terms:
-5 + x = 7.118052168

Solving
-5 + x = 7.118052168

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 = 7.118052168 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.118052168 + 5
x = 7.118052168 + 5

Combine like terms: 7.118052168 + 5 = 12.118052168
x = 12.118052168

Simplifying
x = 12.118052168


Subproblem 2
x + -5 = -7.118052168

Simplifying
x + -5 = -7.118052168

Reorder the terms:
-5 + x = -7.118052168

Solving
-5 + x = -7.118052168

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 = -7.118052168 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.118052168 + 5
x = -7.118052168 + 5

Combine like terms: -7.118052168 + 5 = -2.118052168
x = -2.118052168

Simplifying
x = -2.118052168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.118052168, -2.118052168}

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