3x^2+32x+48=0

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Solution for 3x^2+32x+48=0 equation: 


Simplifying
3x2 + 32x + 48 = 0

Reorder the terms:
48 + 32x + 3x2 = 0

Solving
48 + 32x + 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 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + 10.66666667x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + 10.66666667x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 10.66666667x + x2 = 0 + -16
10.66666667x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
10.66666667x + x2 = -16

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = -16 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = -16 + 28.44444446

Combine like terms: -16 + 28.44444446 = 12.44444446
28.44444446 + 10.66666667x + x2 = 12.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 12.44444446

Calculate the square root of the right side: 3.527668417

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 3.527668417 and -3.527668417.


Subproblem 1
x + 5.333333335 = 3.527668417

Simplifying
x + 5.333333335 = 3.527668417

Reorder the terms:
5.333333335 + x = 3.527668417

Solving
5.333333335 + x = 3.527668417

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = 3.527668417 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = 3.527668417 + -5.333333335
x = 3.527668417 + -5.333333335

Combine like terms: 3.527668417 + -5.333333335 = -1.805664918
x = -1.805664918

Simplifying
x = -1.805664918


Subproblem 2
x + 5.333333335 = -3.527668417

Simplifying
x + 5.333333335 = -3.527668417

Reorder the terms:
5.333333335 + x = -3.527668417

Solving
5.333333335 + x = -3.527668417

Solving for variable 'x'.

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

Add '-5.333333335' to each side of the equation.
5.333333335 + -5.333333335 + x = -3.527668417 + -5.333333335

Combine like terms: 5.333333335 + -5.333333335 = 0.000000000
0.000000000 + x = -3.527668417 + -5.333333335
x = -3.527668417 + -5.333333335

Combine like terms: -3.527668417 + -5.333333335 = -8.861001752
x = -8.861001752

Simplifying
x = -8.861001752


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.805664918, -8.861001752}

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