3x^2+27x-24=0

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Solution for 3x^2+27x-24=0 equation:


Simplifying
3x2 + 27x + -24 = 0

Reorder the terms:
-24 + 27x + 3x2 = 0

Solving
-24 + 27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 9x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + 9x + x2 = 0

Solving
-8 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 9x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 9x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 9x + x2 = 0 + 8
9x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
9x + x2 = 8

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 8 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 8 + 20.25

Combine like terms: 8 + 20.25 = 28.25
20.25 + 9x + x2 = 28.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
x + 4.5 = 5.315072906

Simplifying
x + 4.5 = 5.315072906

Reorder the terms:
4.5 + x = 5.315072906

Solving
4.5 + x = 5.315072906

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.315072906 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.315072906 + -4.5
x = 5.315072906 + -4.5

Combine like terms: 5.315072906 + -4.5 = 0.815072906
x = 0.815072906

Simplifying
x = 0.815072906


Subproblem 2
x + 4.5 = -5.315072906

Simplifying
x + 4.5 = -5.315072906

Reorder the terms:
4.5 + x = -5.315072906

Solving
4.5 + x = -5.315072906

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.315072906 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.315072906 + -4.5
x = -5.315072906 + -4.5

Combine like terms: -5.315072906 + -4.5 = -9.815072906
x = -9.815072906

Simplifying
x = -9.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.815072906, -9.815072906}
Solution
x = {0.815072906, -9.815072906}

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