3x-5-0.5x=1.5x(x-1)+3-0.5

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Solution for 3x-5-0.5x=1.5x(x-1)+3-0.5 equation:


Simplifying
3x + -5 + -0.5x = 1.5x(x + -1) + 3 + -0.5

Reorder the terms:
-5 + 3x + -0.5x = 1.5x(x + -1) + 3 + -0.5

Combine like terms: 3x + -0.5x = 2.5x
-5 + 2.5x = 1.5x(x + -1) + 3 + -0.5

Reorder the terms:
-5 + 2.5x = 1.5x(-1 + x) + 3 + -0.5
-5 + 2.5x = (-1 * 1.5x + x * 1.5x) + 3 + -0.5
-5 + 2.5x = (-1.5x + 1.5x2) + 3 + -0.5

Reorder the terms:
-5 + 2.5x = 3 + -0.5 + -1.5x + 1.5x2

Combine like terms: 3 + -0.5 = 2.5
-5 + 2.5x = 2.5 + -1.5x + 1.5x2

Solving
-5 + 2.5x = 2.5 + -1.5x + 1.5x2

Solving for variable 'x'.

Reorder the terms:
-5 + -2.5 + 2.5x + 1.5x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2

Combine like terms: -5 + -2.5 = -7.5
-7.5 + 2.5x + 1.5x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2

Combine like terms: 2.5x + 1.5x = 4x
-7.5 + 4x + -1.5x2 = 2.5 + -1.5x + 1.5x2 + -2.5 + 1.5x + -1.5x2

Reorder the terms:
-7.5 + 4x + -1.5x2 = 2.5 + -2.5 + -1.5x + 1.5x + 1.5x2 + -1.5x2

Combine like terms: 2.5 + -2.5 = 0.0
-7.5 + 4x + -1.5x2 = 0.0 + -1.5x + 1.5x + 1.5x2 + -1.5x2
-7.5 + 4x + -1.5x2 = -1.5x + 1.5x + 1.5x2 + -1.5x2

Combine like terms: -1.5x + 1.5x = 0.0
-7.5 + 4x + -1.5x2 = 0.0 + 1.5x2 + -1.5x2
-7.5 + 4x + -1.5x2 = 1.5x2 + -1.5x2

Combine like terms: 1.5x2 + -1.5x2 = 0.0
-7.5 + 4x + -1.5x2 = 0.0

Begin completing the square.  Divide all terms by
-1.5 the coefficient of the squared term: 

Divide each side by '-1.5'.
5 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2.666666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -2.666666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2.666666667x + x2 = 0 + -5
-2.666666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2.666666667x + x2 = -5

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -5 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -5 + 1.777777780

Combine like terms: -5 + 1.777777780 = -3.22222222
1.777777780 + -2.666666667x + x2 = -3.22222222

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = -3.22222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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