3x^2-49x-130=

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Solution for 3x^2-49x-130= equation: 


Simplifying
3x2 + -49x + -130 = 0

Reorder the terms:
-130 + -49x + 3x2 = 0

Solving
-130 + -49x + 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'.
-43.33333333 + -16.33333333x + x2 = 0

Move the constant term to the right:

Add '43.33333333' to each side of the equation.
-43.33333333 + -16.33333333x + 43.33333333 + x2 = 0 + 43.33333333

Reorder the terms:
-43.33333333 + 43.33333333 + -16.33333333x + x2 = 0 + 43.33333333

Combine like terms: -43.33333333 + 43.33333333 = 0.00000000
0.00000000 + -16.33333333x + x2 = 0 + 43.33333333
-16.33333333x + x2 = 0 + 43.33333333

Combine like terms: 0 + 43.33333333 = 43.33333333
-16.33333333x + x2 = 43.33333333

The x term is -16.33333333x.  Take half its coefficient (-8.166666665).
Square it (66.69444442) and add it to both sides.

Add '66.69444442' to each side of the equation.
-16.33333333x + 66.69444442 + x2 = 43.33333333 + 66.69444442

Reorder the terms:
66.69444442 + -16.33333333x + x2 = 43.33333333 + 66.69444442

Combine like terms: 43.33333333 + 66.69444442 = 110.02777775
66.69444442 + -16.33333333x + x2 = 110.02777775

Factor a perfect square on the left side:
(x + -8.166666665)(x + -8.166666665) = 110.02777775

Calculate the square root of the right side: 10.48941265

Break this problem into two subproblems by setting 
(x + -8.166666665) equal to 10.48941265 and -10.48941265.


Subproblem 1
x + -8.166666665 = 10.48941265

Simplifying
x + -8.166666665 = 10.48941265

Reorder the terms:
-8.166666665 + x = 10.48941265

Solving
-8.166666665 + x = 10.48941265

Solving for variable 'x'.

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

Add '8.166666665' to each side of the equation.
-8.166666665 + 8.166666665 + x = 10.48941265 + 8.166666665

Combine like terms: -8.166666665 + 8.166666665 = 0.000000000
0.000000000 + x = 10.48941265 + 8.166666665
x = 10.48941265 + 8.166666665

Combine like terms: 10.48941265 + 8.166666665 = 18.656079315
x = 18.656079315

Simplifying
x = 18.656079315


Subproblem 2
x + -8.166666665 = -10.48941265

Simplifying
x + -8.166666665 = -10.48941265

Reorder the terms:
-8.166666665 + x = -10.48941265

Solving
-8.166666665 + x = -10.48941265

Solving for variable 'x'.

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

Add '8.166666665' to each side of the equation.
-8.166666665 + 8.166666665 + x = -10.48941265 + 8.166666665

Combine like terms: -8.166666665 + 8.166666665 = 0.000000000
0.000000000 + x = -10.48941265 + 8.166666665
x = -10.48941265 + 8.166666665

Combine like terms: -10.48941265 + 8.166666665 = -2.322745985
x = -2.322745985

Simplifying
x = -2.322745985


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.656079315, -2.322745985}

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