3x^2+8x-48=0

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Solution for 3x^2+8x-48=0 equation: 


Simplifying
3x2 + 8x + -48 = 0

Reorder the terms:
-48 + 8x + 3x2 = 0

Solving
-48 + 8x + 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 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 2.666666667x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 2.666666667x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 2.666666667x + x2 = 0 + 16
2.666666667x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
2.666666667x + x2 = 16

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 16 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 16 + 1.777777780

Combine like terms: 16 + 1.777777780 = 17.77777778
1.777777780 + 2.666666667x + x2 = 17.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 17.77777778

Calculate the square root of the right side: 4.216370214

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 4.216370214 and -4.216370214.


Subproblem 1
x + 1.333333334 = 4.216370214

Simplifying
x + 1.333333334 = 4.216370214

Reorder the terms:
1.333333334 + x = 4.216370214

Solving
1.333333334 + x = 4.216370214

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 4.216370214 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 4.216370214 + -1.333333334
x = 4.216370214 + -1.333333334

Combine like terms: 4.216370214 + -1.333333334 = 2.88303688
x = 2.88303688

Simplifying
x = 2.88303688


Subproblem 2
x + 1.333333334 = -4.216370214

Simplifying
x + 1.333333334 = -4.216370214

Reorder the terms:
1.333333334 + x = -4.216370214

Solving
1.333333334 + x = -4.216370214

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -4.216370214 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -4.216370214 + -1.333333334
x = -4.216370214 + -1.333333334

Combine like terms: -4.216370214 + -1.333333334 = -5.549703548
x = -5.549703548

Simplifying
x = -5.549703548


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.88303688, -5.549703548}

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