12=-1.5x^2+9x

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Solution for 12=-1.5x^2+9x equation:


Simplifying
12 = -1.5x2 + 9x

Reorder the terms:
12 = 9x + -1.5x2

Solving
12 = 9x + -1.5x2

Solving for variable 'x'.

Reorder the terms:
12 + -9x + 1.5x2 = 9x + -9x + -1.5x2 + 1.5x2

Combine like terms: 9x + -9x = 0
12 + -9x + 1.5x2 = 0 + -1.5x2 + 1.5x2
12 + -9x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
12 + -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'.
8 + -6x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -6x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -6x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -6x + x2 = 0 + -8
-6x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-6x + x2 = -8

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 = -8 + 9

Reorder the terms:
9 + -6x + x2 = -8 + 9

Combine like terms: -8 + 9 = 1
9 + -6x + x2 = 1

Factor a perfect square on the left side:
(x + -3)(x + -3) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -3) equal to 1 and -1.

Subproblem 1

x + -3 = 1 Simplifying x + -3 = 1 Reorder the terms: -3 + x = 1 Solving -3 + x = 1 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 = 1 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1 + 3 x = 1 + 3 Combine like terms: 1 + 3 = 4 x = 4 Simplifying x = 4

Subproblem 2

x + -3 = -1 Simplifying x + -3 = -1 Reorder the terms: -3 + x = -1 Solving -3 + x = -1 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 = -1 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1 + 3 x = -1 + 3 Combine like terms: -1 + 3 = 2 x = 2 Simplifying x = 2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4, 2}

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