(X+0.2)(X+1.5)=0

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Solution for (X+0.2)(X+1.5)=0 equation: 


Simplifying
(X + 0.2)(X + 1.5) = 0

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

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

Multiply (0.2 + X) * (1.5 + X)
(0.2(1.5 + X) + X(1.5 + X)) = 0
((1.5 * 0.2 + X * 0.2) + X(1.5 + X)) = 0
((0.3 + 0.2X) + X(1.5 + X)) = 0
(0.3 + 0.2X + (1.5 * X + X * X)) = 0
(0.3 + 0.2X + (1.5X + X2)) = 0

Combine like terms: 0.2X + 1.5X = 1.7X
(0.3 + 1.7X + X2) = 0

Solving
0.3 + 1.7X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 1.7X + -0.3 + X2 = 0 + -0.3

Reorder the terms:
0.3 + -0.3 + 1.7X + X2 = 0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 1.7X + X2 = 0 + -0.3
1.7X + X2 = 0 + -0.3

Combine like terms: 0 + -0.3 = -0.3
1.7X + X2 = -0.3

The X term is 1.7X.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7X + 0.7225 + X2 = -0.3 + 0.7225

Reorder the terms:
0.7225 + 1.7X + X2 = -0.3 + 0.7225

Combine like terms: -0.3 + 0.7225 = 0.4225
0.7225 + 1.7X + X2 = 0.4225

Factor a perfect square on the left side:
(X + 0.85)(X + 0.85) = 0.4225

Calculate the square root of the right side: 0.65

Break this problem into two subproblems by setting 
(X + 0.85) equal to 0.65 and -0.65.


Subproblem 1
X + 0.85 = 0.65

Simplifying
X + 0.85 = 0.65

Reorder the terms:
0.85 + X = 0.65

Solving
0.85 + X = 0.65

Solving for variable 'X'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + X = 0.65 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + X = 0.65 + -0.85
X = 0.65 + -0.85

Combine like terms: 0.65 + -0.85 = -0.2
X = -0.2

Simplifying
X = -0.2


Subproblem 2
X + 0.85 = -0.65

Simplifying
X + 0.85 = -0.65

Reorder the terms:
0.85 + X = -0.65

Solving
0.85 + X = -0.65

Solving for variable 'X'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + X = -0.65 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + X = -0.65 + -0.85
X = -0.65 + -0.85

Combine like terms: -0.65 + -0.85 = -1.5
X = -1.5

Simplifying
X = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-0.2, -1.5}

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