3x^2+2x-48=0

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


Simplifying
3x2 + 2x + -48 = 0

Reorder the terms:
-48 + 2x + 3x2 = 0

Solving
-48 + 2x + 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 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.6666666667x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.6666666667x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.6666666667x + x2 = 0 + 16
0.6666666667x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.6666666667x + x2 = 16

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 16 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 16 + 0.1111111112

Combine like terms: 16 + 0.1111111112 = 16.1111111112
0.1111111112 + 0.6666666667x + x2 = 16.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 16.1111111112

Calculate the square root of the right side: 4.01386486

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 4.01386486 and -4.01386486.


Subproblem 1
x + 0.3333333334 = 4.01386486

Simplifying
x + 0.3333333334 = 4.01386486

Reorder the terms:
0.3333333334 + x = 4.01386486

Solving
0.3333333334 + x = 4.01386486

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 4.01386486 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 4.01386486 + -0.3333333334
x = 4.01386486 + -0.3333333334

Combine like terms: 4.01386486 + -0.3333333334 = 3.6805315266
x = 3.6805315266

Simplifying
x = 3.6805315266


Subproblem 2
x + 0.3333333334 = -4.01386486

Simplifying
x + 0.3333333334 = -4.01386486

Reorder the terms:
0.3333333334 + x = -4.01386486

Solving
0.3333333334 + x = -4.01386486

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -4.01386486 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -4.01386486 + -0.3333333334
x = -4.01386486 + -0.3333333334

Combine like terms: -4.01386486 + -0.3333333334 = -4.3471981934
x = -4.3471981934

Simplifying
x = -4.3471981934


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.6805315266, -4.3471981934}

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