x=1.5x^2-8x-.5*2

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Solution for x=1.5x^2-8x-.5*2 equation:


Simplifying
x = 1.5x2 + -8x + -0.5 * 2

Multiply -0.5 * 2
x = 1.5x2 + -8x + -1

Reorder the terms:
x = -1 + -8x + 1.5x2

Solving
x = -1 + -8x + 1.5x2

Solving for variable 'x'.

Reorder the terms:
1 + x + 8x + -1.5x2 = -1 + -8x + 1.5x2 + 1 + 8x + -1.5x2

Combine like terms: x + 8x = 9x
1 + 9x + -1.5x2 = -1 + -8x + 1.5x2 + 1 + 8x + -1.5x2

Reorder the terms:
1 + 9x + -1.5x2 = -1 + 1 + -8x + 8x + 1.5x2 + -1.5x2

Combine like terms: -1 + 1 = 0
1 + 9x + -1.5x2 = 0 + -8x + 8x + 1.5x2 + -1.5x2
1 + 9x + -1.5x2 = -8x + 8x + 1.5x2 + -1.5x2

Combine like terms: -8x + 8x = 0
1 + 9x + -1.5x2 = 0 + 1.5x2 + -1.5x2
1 + 9x + -1.5x2 = 1.5x2 + -1.5x2

Combine like terms: 1.5x2 + -1.5x2 = 0.0
1 + 9x + -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'.
-0.6666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -6x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -6x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -6x + x2 = 0 + 0.6666666667
-6x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-6x + x2 = 0.6666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 0.6666666667 + 9

Reorder the terms:
9 + -6x + x2 = 0.6666666667 + 9

Combine like terms: 0.6666666667 + 9 = 9.6666666667
9 + -6x + x2 = 9.6666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 9.6666666667

Calculate the square root of the right side: 3.109126351

Break this problem into two subproblems by setting 
(x + -3) equal to 3.109126351 and -3.109126351.

Subproblem 1

x + -3 = 3.109126351 Simplifying x + -3 = 3.109126351 Reorder the terms: -3 + x = 3.109126351 Solving -3 + x = 3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.109126351 + 3 x = 3.109126351 + 3 Combine like terms: 3.109126351 + 3 = 6.109126351 x = 6.109126351 Simplifying x = 6.109126351

Subproblem 2

x + -3 = -3.109126351 Simplifying x + -3 = -3.109126351 Reorder the terms: -3 + x = -3.109126351 Solving -3 + x = -3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.109126351 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.109126351 + 3 x = -3.109126351 + 3 Combine like terms: -3.109126351 + 3 = -0.109126351 x = -0.109126351 Simplifying x = -0.109126351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.109126351, -0.109126351}

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