12x=6-3x^2

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Solution for 12x=6-3x^2 equation:


Simplifying
12x = 6 + -3x2

Solving
12x = 6 + -3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 12x + 3x2 = 6 + -3x2 + -6 + 3x2

Reorder the terms:
-6 + 12x + 3x2 = 6 + -6 + -3x2 + 3x2

Combine like terms: 6 + -6 = 0
-6 + 12x + 3x2 = 0 + -3x2 + 3x2
-6 + 12x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-6 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + 4x + x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + x2 = 0 Solving -2 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + x2 = 0 + 2 4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + x2 = 2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 2 + 4 Reorder the terms: 4 + 4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4x + x2 = 6 Factor a perfect square on the left side: (x + 2)(x + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 2) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + 2 = 2.449489743 Simplifying x + 2 = 2.449489743 Reorder the terms: 2 + x = 2.449489743 Solving 2 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.449489743 + -2 x = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 x = 0.449489743 Simplifying x = 0.449489743

Subproblem 2

x + 2 = -2.449489743 Simplifying x + 2 = -2.449489743 Reorder the terms: 2 + x = -2.449489743 Solving 2 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.449489743 + -2 x = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 x = -4.449489743 Simplifying x = -4.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.449489743, -4.449489743}

Solution

x = {0.449489743, -4.449489743}

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