3x^2+21x+27=0

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Solution for 3x^2+21x+27=0 equation: 


Simplifying
3x2 + 21x + 27 = 0

Reorder the terms:
27 + 21x + 3x2 = 0

Solving
27 + 21x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 7x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 7x + x2 = 0

Solving
9 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 7x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 7x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7x + x2 = 0 + -9
7x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
7x + x2 = -9

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -9 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -9 + 12.25

Combine like terms: -9 + 12.25 = 3.25
12.25 + 7x + x2 = 3.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 3.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 3.5 = 1.802775638

Simplifying
x + 3.5 = 1.802775638

Reorder the terms:
3.5 + x = 1.802775638

Solving
3.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 1.802775638 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 1.802775638 + -3.5
x = 1.802775638 + -3.5

Combine like terms: 1.802775638 + -3.5 = -1.697224362
x = -1.697224362

Simplifying
x = -1.697224362


Subproblem 2
x + 3.5 = -1.802775638

Simplifying
x + 3.5 = -1.802775638

Reorder the terms:
3.5 + x = -1.802775638

Solving
3.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -1.802775638 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -1.802775638 + -3.5
x = -1.802775638 + -3.5

Combine like terms: -1.802775638 + -3.5 = -5.302775638
x = -5.302775638

Simplifying
x = -5.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.697224362, -5.302775638}
Solution
x = {-1.697224362, -5.302775638}

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