(1.2X+1)(0.8X+1)=0

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Solution for (1.2X+1)(0.8X+1)=0 equation:


Simplifying
(1.2X + 1)(0.8X + 1) = 0

Reorder the terms:
(1 + 1.2X)(0.8X + 1) = 0

Reorder the terms:
(1 + 1.2X)(1 + 0.8X) = 0

Multiply (1 + 1.2X) * (1 + 0.8X)
(1(1 + 0.8X) + 1.2X * (1 + 0.8X)) = 0
((1 * 1 + 0.8X * 1) + 1.2X * (1 + 0.8X)) = 0
((1 + 0.8X) + 1.2X * (1 + 0.8X)) = 0
(1 + 0.8X + (1 * 1.2X + 0.8X * 1.2X)) = 0
(1 + 0.8X + (1.2X + 0.96X2)) = 0

Combine like terms: 0.8X + 1.2X = 2X
(1 + 2X + 0.96X2) = 0

Solving
1 + 2X + 0.96X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
0.96 the coefficient of the squared term: 

Divide each side by '0.96'.
1.041666667 + 2.083333333X + X2 = 0

Move the constant term to the right:

Add '-1.041666667' to each side of the equation.
1.041666667 + 2.083333333X + -1.041666667 + X2 = 0 + -1.041666667

Reorder the terms:
1.041666667 + -1.041666667 + 2.083333333X + X2 = 0 + -1.041666667

Combine like terms: 1.041666667 + -1.041666667 = 0.000000000
0.000000000 + 2.083333333X + X2 = 0 + -1.041666667
2.083333333X + X2 = 0 + -1.041666667

Combine like terms: 0 + -1.041666667 = -1.041666667
2.083333333X + X2 = -1.041666667

The X term is 2.083333333X.  Take half its coefficient (1.041666667).
Square it (1.085069445) and add it to both sides.

Add '1.085069445' to each side of the equation.
2.083333333X + 1.085069445 + X2 = -1.041666667 + 1.085069445

Reorder the terms:
1.085069445 + 2.083333333X + X2 = -1.041666667 + 1.085069445

Combine like terms: -1.041666667 + 1.085069445 = 0.043402778
1.085069445 + 2.083333333X + X2 = 0.043402778

Factor a perfect square on the left side:
(X + 1.041666667)(X + 1.041666667) = 0.043402778

Calculate the square root of the right side: 0.208333334

Break this problem into two subproblems by setting 
(X + 1.041666667) equal to 0.208333334 and -0.208333334.

Subproblem 1

X + 1.041666667 = 0.208333334 Simplifying X + 1.041666667 = 0.208333334 Reorder the terms: 1.041666667 + X = 0.208333334 Solving 1.041666667 + X = 0.208333334 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + X = 0.208333334 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + X = 0.208333334 + -1.041666667 X = 0.208333334 + -1.041666667 Combine like terms: 0.208333334 + -1.041666667 = -0.833333333 X = -0.833333333 Simplifying X = -0.833333333

Subproblem 2

X + 1.041666667 = -0.208333334 Simplifying X + 1.041666667 = -0.208333334 Reorder the terms: 1.041666667 + X = -0.208333334 Solving 1.041666667 + X = -0.208333334 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.041666667' to each side of the equation. 1.041666667 + -1.041666667 + X = -0.208333334 + -1.041666667 Combine like terms: 1.041666667 + -1.041666667 = 0.000000000 0.000000000 + X = -0.208333334 + -1.041666667 X = -0.208333334 + -1.041666667 Combine like terms: -0.208333334 + -1.041666667 = -1.250000001 X = -1.250000001 Simplifying X = -1.250000001

Solution

The solution to the problem is based on the solutions from the subproblems. X = {-0.833333333, -1.250000001}

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