(X+1.5)(X+8)=0

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Solution for (X+1.5)(X+8)=0 equation: 


Simplifying
(X + 1.5)(X + 8) = 0

Reorder the terms:
(1.5 + X)(X + 8) = 0

Reorder the terms:
(1.5 + X)(8 + X) = 0

Multiply (1.5 + X) * (8 + X)
(1.5(8 + X) + X(8 + X)) = 0
((8 * 1.5 + X * 1.5) + X(8 + X)) = 0
((12 + 1.5X) + X(8 + X)) = 0
(12 + 1.5X + (8 * X + X * X)) = 0
(12 + 1.5X + (8X + X2)) = 0

Combine like terms: 1.5X + 8X = 9.5X
(12 + 9.5X + X2) = 0

Solving
12 + 9.5X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 9.5X + -12 + X2 = 0 + -12

Reorder the terms:
12 + -12 + 9.5X + X2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 9.5X + X2 = 0 + -12
9.5X + X2 = 0 + -12

Combine like terms: 0 + -12 = -12
9.5X + X2 = -12

The X term is 9.5X.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5X + 22.5625 + X2 = -12 + 22.5625

Reorder the terms:
22.5625 + 9.5X + X2 = -12 + 22.5625

Combine like terms: -12 + 22.5625 = 10.5625
22.5625 + 9.5X + X2 = 10.5625

Factor a perfect square on the left side:
(X + 4.75)(X + 4.75) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(X + 4.75) equal to 3.25 and -3.25.


Subproblem 1
X + 4.75 = 3.25

Simplifying
X + 4.75 = 3.25

Reorder the terms:
4.75 + X = 3.25

Solving
4.75 + X = 3.25

Solving for variable 'X'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + X = 3.25 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + X = 3.25 + -4.75
X = 3.25 + -4.75

Combine like terms: 3.25 + -4.75 = -1.5
X = -1.5

Simplifying
X = -1.5


Subproblem 2
X + 4.75 = -3.25

Simplifying
X + 4.75 = -3.25

Reorder the terms:
4.75 + X = -3.25

Solving
4.75 + X = -3.25

Solving for variable 'X'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + X = -3.25 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + X = -3.25 + -4.75
X = -3.25 + -4.75

Combine like terms: -3.25 + -4.75 = -8
X = -8

Simplifying
X = -8


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-1.5, -8}

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