3x^2+24x+27=0

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


Simplifying
3x2 + 24x + 27 = 0

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

Solving
27 + 24x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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

Simplifying
9 + 8x + x2 = 0

Solving
9 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -9 + 16

Reorder the terms:
16 + 8x + x2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8x + x2 = 7

Factor a perfect square on the left side:
(x + 4)(x + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 4) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + 4 = 2.645751311

Simplifying
x + 4 = 2.645751311

Reorder the terms:
4 + x = 2.645751311

Solving
4 + x = 2.645751311

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + x = 2.645751311 + -4
x = 2.645751311 + -4

Combine like terms: 2.645751311 + -4 = -1.354248689
x = -1.354248689

Simplifying
x = -1.354248689


Subproblem 2
x + 4 = -2.645751311

Simplifying
x + 4 = -2.645751311

Reorder the terms:
4 + x = -2.645751311

Solving
4 + x = -2.645751311

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + x = -2.645751311 + -4
x = -2.645751311 + -4

Combine like terms: -2.645751311 + -4 = -6.645751311
x = -6.645751311

Simplifying
x = -6.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.354248689, -6.645751311}
Solution
x = {-1.354248689, -6.645751311}

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