x^2+4.5x+2=0

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Solution for x^2+4.5x+2=0 equation: 


Simplifying
x2 + 4.5x + 2 = 0

Reorder the terms:
2 + 4.5x + x2 = 0

Solving
2 + 4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 4.5x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 4.5x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4.5x + x2 = 0 + -2
4.5x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
4.5x + x2 = -2

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -2 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -2 + 5.0625

Combine like terms: -2 + 5.0625 = 3.0625
5.0625 + 4.5x + x2 = 3.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 3.0625

Calculate the square root of the right side: 1.75

Break this problem into two subproblems by setting 
(x + 2.25) equal to 1.75 and -1.75.


Subproblem 1
x + 2.25 = 1.75

Simplifying
x + 2.25 = 1.75

Reorder the terms:
2.25 + x = 1.75

Solving
2.25 + x = 1.75

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 1.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 1.75 + -2.25
x = 1.75 + -2.25

Combine like terms: 1.75 + -2.25 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 2.25 = -1.75

Simplifying
x + 2.25 = -1.75

Reorder the terms:
2.25 + x = -1.75

Solving
2.25 + x = -1.75

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -1.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -1.75 + -2.25
x = -1.75 + -2.25

Combine like terms: -1.75 + -2.25 = -4
x = -4

Simplifying
x = -4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -4}

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