x^2+3x+2.16=0

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Solution for x^2+3x+2.16=0 equation: 


Simplifying
x2 + 3x + 2.16 = 0

Reorder the terms:
2.16 + 3x + x2 = 0

Solving
2.16 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.16' to each side of the equation.
2.16 + 3x + -2.16 + x2 = 0 + -2.16

Reorder the terms:
2.16 + -2.16 + 3x + x2 = 0 + -2.16

Combine like terms: 2.16 + -2.16 = 0.00
0.00 + 3x + x2 = 0 + -2.16
3x + x2 = 0 + -2.16

Combine like terms: 0 + -2.16 = -2.16
3x + x2 = -2.16

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -2.16 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -2.16 + 2.25

Combine like terms: -2.16 + 2.25 = 0.09
2.25 + 3x + x2 = 0.09

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.09

Calculate the square root of the right side: 0.3

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.3 and -0.3.


Subproblem 1
x + 1.5 = 0.3

Simplifying
x + 1.5 = 0.3

Reorder the terms:
1.5 + x = 0.3

Solving
1.5 + x = 0.3

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 0.3 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 0.3 + -1.5
x = 0.3 + -1.5

Combine like terms: 0.3 + -1.5 = -1.2
x = -1.2

Simplifying
x = -1.2


Subproblem 2
x + 1.5 = -0.3

Simplifying
x + 1.5 = -0.3

Reorder the terms:
1.5 + x = -0.3

Solving
1.5 + x = -0.3

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -0.3 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -0.3 + -1.5
x = -0.3 + -1.5

Combine like terms: -0.3 + -1.5 = -1.8
x = -1.8

Simplifying
x = -1.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.2, -1.8}

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