x^2+4.5x-28=0

Solution for x^2+4.5x-28=0 equation:

Simplifying
x2 + 4.5x + -28 = 0

Reorder the terms:
-28 + 4.5x + x2 = 0

Solving
-28 + 4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 4.5x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 4.5x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 4.5x + x2 = 0 + 28
4.5x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
4.5x + x2 = 28

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 = 28 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 28 + 5.0625

Combine like terms: 28 + 5.0625 = 33.0625
5.0625 + 4.5x + x2 = 33.0625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 33.0625

Calculate the square root of the right side: 5.75

Break this problem into two subproblems by setting 
(x + 2.25) equal to 5.75 and -5.75.

Subproblem 1
x + 2.25 = 5.75

Simplifying
x + 2.25 = 5.75

Reorder the terms:
2.25 + x = 5.75

Solving
2.25 + x = 5.75

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 = 5.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 5.75 + -2.25
x = 5.75 + -2.25

Combine like terms: 5.75 + -2.25 = 3.5
x = 3.5

Simplifying
x = 3.5

Subproblem 2
x + 2.25 = -5.75

Simplifying
x + 2.25 = -5.75

Reorder the terms:
2.25 + x = -5.75

Solving
2.25 + x = -5.75

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 = -5.75 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -5.75 + -2.25
x = -5.75 + -2.25

Combine like terms: -5.75 + -2.25 = -8
x = -8

Simplifying
x = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -8}