x^2+3x+2.24=0

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Solution for x^2+3x+2.24=0 equation:


Simplifying
x2 + 3x + 2.24 = 0

Reorder the terms:
2.24 + 3x + x2 = 0

Solving
2.24 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.24' to each side of the equation.
2.24 + 3x + -2.24 + x2 = 0 + -2.24

Reorder the terms:
2.24 + -2.24 + 3x + x2 = 0 + -2.24

Combine like terms: 2.24 + -2.24 = 0.00
0.00 + 3x + x2 = 0 + -2.24
3x + x2 = 0 + -2.24

Combine like terms: 0 + -2.24 = -2.24
3x + x2 = -2.24

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 = -2.24 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -2.24 + 2.25

Combine like terms: -2.24 + 2.25 = 0.01
2.25 + 3x + x2 = 0.01

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.1 and -0.1.


Subproblem 1
x + 1.5 = 0.1

Simplifying
x + 1.5 = 0.1

Reorder the terms:
1.5 + x = 0.1

Solving
1.5 + x = 0.1

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 = 0.1 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 0.1 + -1.5
x = 0.1 + -1.5

Combine like terms: 0.1 + -1.5 = -1.4
x = -1.4

Simplifying
x = -1.4


Subproblem 2
x + 1.5 = -0.1

Simplifying
x + 1.5 = -0.1

Reorder the terms:
1.5 + x = -0.1

Solving
1.5 + x = -0.1

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 = -0.1 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -0.1 + -1.5
x = -0.1 + -1.5

Combine like terms: -0.1 + -1.5 = -1.6
x = -1.6

Simplifying
x = -1.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.4, -1.6}

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