12x=3x^2-81

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Solution for 12x=3x^2-81 equation:


Simplifying
12x = 3x2 + -81

Reorder the terms:
12x = -81 + 3x2

Solving
12x = -81 + 3x2

Solving for variable 'x'.

Reorder the terms:
81 + 12x + -3x2 = -81 + 3x2 + 81 + -3x2

Reorder the terms:
81 + 12x + -3x2 = -81 + 81 + 3x2 + -3x2

Combine like terms: -81 + 81 = 0
81 + 12x + -3x2 = 0 + 3x2 + -3x2
81 + 12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
81 + 12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + 4x + -1x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(27 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying 27 + 4x + -1x2 = 0 Solving 27 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -4x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -4x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -4x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -4x + x2 = 0 + 27 -4x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -4x + x2 = 27 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 = 27 + 4 Reorder the terms: 4 + -4x + x2 = 27 + 4 Combine like terms: 27 + 4 = 31 4 + -4x + x2 = 31 Factor a perfect square on the left side: (x + -2)(x + -2) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -2) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + -2 = 5.567764363 Simplifying x + -2 = 5.567764363 Reorder the terms: -2 + x = 5.567764363 Solving -2 + x = 5.567764363 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 = 5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.567764363 + 2 x = 5.567764363 + 2 Combine like terms: 5.567764363 + 2 = 7.567764363 x = 7.567764363 Simplifying x = 7.567764363

Subproblem 2

x + -2 = -5.567764363 Simplifying x + -2 = -5.567764363 Reorder the terms: -2 + x = -5.567764363 Solving -2 + x = -5.567764363 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 = -5.567764363 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.567764363 + 2 x = -5.567764363 + 2 Combine like terms: -5.567764363 + 2 = -3.567764363 x = -3.567764363 Simplifying x = -3.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.567764363, -3.567764363}

Solution

x = {7.567764363, -3.567764363}

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