x^2+4.5x=2.5

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Solution for x^2+4.5x=2.5 equation: 


Simplifying
x2 + 4.5x = 2.5

Reorder the terms:
4.5x + x2 = 2.5

Solving
4.5x + x2 = 2.5

Solving for variable 'x'.

Reorder the terms:
-2.5 + 4.5x + x2 = 2.5 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
-2.5 + 4.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 4.5x + 2.5 + x2 = 0.0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 4.5x + x2 = 0.0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 4.5x + x2 = 0.0 + 2.5
4.5x + x2 = 0.0 + 2.5

Combine like terms: 0.0 + 2.5 = 2.5
4.5x + x2 = 2.5

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 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 2.5 + 5.0625

Combine like terms: 2.5 + 5.0625 = 7.5625
5.0625 + 4.5x + x2 = 7.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 7.5625

Calculate the square root of the right side: 2.75

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.75 and -2.75.


Subproblem 1
x + 2.25 = 2.75

Simplifying
x + 2.25 = 2.75

Reorder the terms:
2.25 + x = 2.75

Solving
2.25 + x = 2.75

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 = 2.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.75 + -2.25
x = 2.75 + -2.25

Combine like terms: 2.75 + -2.25 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 2.25 = -2.75

Simplifying
x + 2.25 = -2.75

Reorder the terms:
2.25 + x = -2.75

Solving
2.25 + x = -2.75

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 = -2.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.75 + -2.25
x = -2.75 + -2.25

Combine like terms: -2.75 + -2.25 = -5
x = -5

Simplifying
x = -5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -5}

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