2.25-3x+x^2=18

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Solution for 2.25-3x+x^2=18 equation: 


Simplifying
2.25 + -3x + x2 = 18

Solving
2.25 + -3x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
2.25 + -18 + -3x + x2 = 18 + -18

Combine like terms: 2.25 + -18 = -15.75
-15.75 + -3x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-15.75 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + -3x + 15.75 + x2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + -3x + x2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + -3x + x2 = 0 + 15.75
-3x + x2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
-3x + x2 = 15.75

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 = 15.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 15.75 + 2.25

Combine like terms: 15.75 + 2.25 = 18
2.25 + -3x + x2 = 18

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -1.5 = 4.242640687

Simplifying
x + -1.5 = 4.242640687

Reorder the terms:
-1.5 + x = 4.242640687

Solving
-1.5 + x = 4.242640687

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 = 4.242640687 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.242640687 + 1.5
x = 4.242640687 + 1.5

Combine like terms: 4.242640687 + 1.5 = 5.742640687
x = 5.742640687

Simplifying
x = 5.742640687


Subproblem 2
x + -1.5 = -4.242640687

Simplifying
x + -1.5 = -4.242640687

Reorder the terms:
-1.5 + x = -4.242640687

Solving
-1.5 + x = -4.242640687

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 = -4.242640687 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.242640687 + 1.5
x = -4.242640687 + 1.5

Combine like terms: -4.242640687 + 1.5 = -2.742640687
x = -2.742640687

Simplifying
x = -2.742640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.742640687, -2.742640687}

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