0=12+3x-x^2

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Solution for 0=12+3x-x^2 equation:


Simplifying
0 = 12 + 3x + -1x2

Solving
0 = 12 + 3x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -3x + x2 = 12 + 3x + -1x2 + -12 + -3x + x2

Reorder the terms:
-12 + -3x + x2 = 12 + -12 + 3x + -3x + -1x2 + x2

Combine like terms: 12 + -12 = 0
-12 + -3x + x2 = 0 + 3x + -3x + -1x2 + x2
-12 + -3x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
-12 + -3x + x2 = 0 + -1x2 + x2
-12 + -3x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -3x + x2 = 0 + 12
-3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3x + x2 = 12

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 12 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3x + x2 = 14.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -1.5 = 3.774917218 Simplifying x + -1.5 = 3.774917218 Reorder the terms: -1.5 + x = 3.774917218 Solving -1.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.774917218 + 1.5 x = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 x = 5.274917218 Simplifying x = 5.274917218

Subproblem 2

x + -1.5 = -3.774917218 Simplifying x + -1.5 = -3.774917218 Reorder the terms: -1.5 + x = -3.774917218 Solving -1.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.774917218 + 1.5 x = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 x = -2.274917218 Simplifying x = -2.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.274917218, -2.274917218}

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