x^2+5x+2.25=0

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Solution for x^2+5x+2.25=0 equation: 


Simplifying
x2 + 5x + 2.25 = 0

Reorder the terms:
2.25 + 5x + x2 = 0

Solving
2.25 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 5x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 5x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 5x + x2 = 0 + -2.25
5x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
5x + x2 = -2.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -2.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -2.25 + 6.25

Combine like terms: -2.25 + 6.25 = 4
6.25 + 5x + x2 = 4

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2 and -2.


Subproblem 1
x + 2.5 = 2

Simplifying
x + 2.5 = 2

Reorder the terms:
2.5 + x = 2

Solving
2.5 + x = 2

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2 + -2.5
x = 2 + -2.5

Combine like terms: 2 + -2.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 2.5 = -2

Simplifying
x + 2.5 = -2

Reorder the terms:
2.5 + x = -2

Solving
2.5 + x = -2

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2 + -2.5
x = -2 + -2.5

Combine like terms: -2 + -2.5 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -4.5}

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