2x(1-x)-3x(x-1)=-18

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Solution for 2x(1-x)-3x(x-1)=-18 equation:


Simplifying
2x(1 + -1x) + -3x(x + -1) = -18
(1 * 2x + -1x * 2x) + -3x(x + -1) = -18
(2x + -2x2) + -3x(x + -1) = -18

Reorder the terms:
2x + -2x2 + -3x(-1 + x) = -18
2x + -2x2 + (-1 * -3x + x * -3x) = -18
2x + -2x2 + (3x + -3x2) = -18

Reorder the terms:
2x + 3x + -2x2 + -3x2 = -18

Combine like terms: 2x + 3x = 5x
5x + -2x2 + -3x2 = -18

Combine like terms: -2x2 + -3x2 = -5x2
5x + -5x2 = -18

Solving
5x + -5x2 = -18

Solving for variable 'x'.

Reorder the terms:
18 + 5x + -5x2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + 5x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-3.6 + -1x + x2 = 0

Move the constant term to the right:

Add '3.6' to each side of the equation.
-3.6 + -1x + 3.6 + x2 = 0 + 3.6

Reorder the terms:
-3.6 + 3.6 + -1x + x2 = 0 + 3.6

Combine like terms: -3.6 + 3.6 = 0.0
0.0 + -1x + x2 = 0 + 3.6
-1x + x2 = 0 + 3.6

Combine like terms: 0 + 3.6 = 3.6
-1x + x2 = 3.6

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.6 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.6 + 0.25

Combine like terms: 3.6 + 0.25 = 3.85
0.25 + -1x + x2 = 3.85

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.85

Calculate the square root of the right side: 1.962141687

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.962141687 and -1.962141687.

Subproblem 1

x + -0.5 = 1.962141687 Simplifying x + -0.5 = 1.962141687 Reorder the terms: -0.5 + x = 1.962141687 Solving -0.5 + x = 1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.962141687 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.962141687 + 0.5 x = 1.962141687 + 0.5 Combine like terms: 1.962141687 + 0.5 = 2.462141687 x = 2.462141687 Simplifying x = 2.462141687

Subproblem 2

x + -0.5 = -1.962141687 Simplifying x + -0.5 = -1.962141687 Reorder the terms: -0.5 + x = -1.962141687 Solving -0.5 + x = -1.962141687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.962141687 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.962141687 + 0.5 x = -1.962141687 + 0.5 Combine like terms: -1.962141687 + 0.5 = -1.462141687 x = -1.462141687 Simplifying x = -1.462141687

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.462141687, -1.462141687}

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