3x^2+8x-224=0

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Solution for 3x^2+8x-224=0 equation: 


Simplifying
3x2 + 8x + -224 = 0

Reorder the terms:
-224 + 8x + 3x2 = 0

Solving
-224 + 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'.
-74.66666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '74.66666667' to each side of the equation.
-74.66666667 + 2.666666667x + 74.66666667 + x2 = 0 + 74.66666667

Reorder the terms:
-74.66666667 + 74.66666667 + 2.666666667x + x2 = 0 + 74.66666667

Combine like terms: -74.66666667 + 74.66666667 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 74.66666667
2.666666667x + x2 = 0 + 74.66666667

Combine like terms: 0 + 74.66666667 = 74.66666667
2.666666667x + x2 = 74.66666667

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 = 74.66666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 74.66666667 + 1.777777780

Combine like terms: 74.66666667 + 1.777777780 = 76.44444445
1.777777780 + 2.666666667x + x2 = 76.44444445

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 76.44444445

Calculate the square root of the right side: 8.743251366

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 8.743251366 and -8.743251366.


Subproblem 1
x + 1.333333334 = 8.743251366

Simplifying
x + 1.333333334 = 8.743251366

Reorder the terms:
1.333333334 + x = 8.743251366

Solving
1.333333334 + x = 8.743251366

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 = 8.743251366 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 8.743251366 + -1.333333334
x = 8.743251366 + -1.333333334

Combine like terms: 8.743251366 + -1.333333334 = 7.409918032
x = 7.409918032

Simplifying
x = 7.409918032


Subproblem 2
x + 1.333333334 = -8.743251366

Simplifying
x + 1.333333334 = -8.743251366

Reorder the terms:
1.333333334 + x = -8.743251366

Solving
1.333333334 + x = -8.743251366

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 = -8.743251366 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -8.743251366 + -1.333333334
x = -8.743251366 + -1.333333334

Combine like terms: -8.743251366 + -1.333333334 = -10.0765847
x = -10.0765847

Simplifying
x = -10.0765847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.409918032, -10.0765847}

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