(1.5+X)*(3.0+X)=9

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Solution for (1.5+X)*(3.0+X)=9 equation: 


Simplifying
(1.5 + X)(3.0 + X) = 9

Multiply (1.5 + X) * (3.0 + X)
(1.5(3.0 + X) + X(3.0 + X)) = 9
((3.0 * 1.5 + X * 1.5) + X(3.0 + X)) = 9
((4.5 + 1.5X) + X(3.0 + X)) = 9
(4.5 + 1.5X + (3.0 * X + X * X)) = 9
(4.5 + 1.5X + (3.0X + X2)) = 9

Combine like terms: 1.5X + 3.0X = 4.5X
(4.5 + 4.5X + X2) = 9

Solving
4.5 + 4.5X + X2 = 9

Solving for variable 'X'.

Reorder the terms:
4.5 + -9 + 4.5X + X2 = 9 + -9

Combine like terms: 4.5 + -9 = -4.5
-4.5 + 4.5X + X2 = 9 + -9

Combine like terms: 9 + -9 = 0
-4.5 + 4.5X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 4.5X + 4.5 + X2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 4.5X + X2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 4.5X + X2 = 0 + 4.5
4.5X + X2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
4.5X + X2 = 4.5

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 = 4.5 + 5.0625

Reorder the terms:
5.0625 + 4.5X + X2 = 4.5 + 5.0625

Combine like terms: 4.5 + 5.0625 = 9.5625
5.0625 + 4.5X + X2 = 9.5625

Factor a perfect square on the left side:
(X + 2.25)(X + 2.25) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(X + 2.25) equal to 3.092329219 and -3.092329219.


Subproblem 1
X + 2.25 = 3.092329219

Simplifying
X + 2.25 = 3.092329219

Reorder the terms:
2.25 + X = 3.092329219

Solving
2.25 + X = 3.092329219

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 = 3.092329219 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + X = 3.092329219 + -2.25
X = 3.092329219 + -2.25

Combine like terms: 3.092329219 + -2.25 = 0.842329219
X = 0.842329219

Simplifying
X = 0.842329219


Subproblem 2
X + 2.25 = -3.092329219

Simplifying
X + 2.25 = -3.092329219

Reorder the terms:
2.25 + X = -3.092329219

Solving
2.25 + X = -3.092329219

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 = -3.092329219 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + X = -3.092329219 + -2.25
X = -3.092329219 + -2.25

Combine like terms: -3.092329219 + -2.25 = -5.342329219
X = -5.342329219

Simplifying
X = -5.342329219


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.842329219, -5.342329219}

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