3x^2-11x-48=0

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Solution for 3x^2-11x-48=0 equation: 


Simplifying
3x2 + -11x + -48 = 0

Reorder the terms:
-48 + -11x + 3x2 = 0

Solving
-48 + -11x + 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'.
-16 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -3.666666667x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -3.666666667x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3.666666667x + x2 = 0 + 16
-3.666666667x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-3.666666667x + x2 = 16

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 16 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 16 + 3.361111114

Combine like terms: 16 + 3.361111114 = 19.361111114
3.361111114 + -3.666666667x + x2 = 19.361111114

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 19.361111114

Calculate the square root of the right side: 4.400126261

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 4.400126261 and -4.400126261.


Subproblem 1
x + -1.833333334 = 4.400126261

Simplifying
x + -1.833333334 = 4.400126261

Reorder the terms:
-1.833333334 + x = 4.400126261

Solving
-1.833333334 + x = 4.400126261

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 4.400126261 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 4.400126261 + 1.833333334
x = 4.400126261 + 1.833333334

Combine like terms: 4.400126261 + 1.833333334 = 6.233459595
x = 6.233459595

Simplifying
x = 6.233459595


Subproblem 2
x + -1.833333334 = -4.400126261

Simplifying
x + -1.833333334 = -4.400126261

Reorder the terms:
-1.833333334 + x = -4.400126261

Solving
-1.833333334 + x = -4.400126261

Solving for variable 'x'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -4.400126261 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -4.400126261 + 1.833333334
x = -4.400126261 + 1.833333334

Combine like terms: -4.400126261 + 1.833333334 = -2.566792927
x = -2.566792927

Simplifying
x = -2.566792927


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.233459595, -2.566792927}

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