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Simplifying x3 + -12x2 + 3x = 0 Reorder the terms: 3x + -12x2 + x3 = 0 Solving 3x + -12x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -12x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + -12x + x2)' equal to zero and attempt to solve: Simplifying 3 + -12x + x2 = 0 Solving 3 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -12x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -12x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -12x + x2 = 0 + -3 -12x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -12x + x2 = -3 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -3 + 36 Reorder the terms: 36 + -12x + x2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + -12x + x2 = 33 Factor a perfect square on the left side: (x + -6)(x + -6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -6) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -6 = 5.744562647 Simplifying x + -6 = 5.744562647 Reorder the terms: -6 + x = 5.744562647 Solving -6 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.744562647 + 6 x = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 x = 11.744562647 Simplifying x = 11.744562647Subproblem 2
x + -6 = -5.744562647 Simplifying x + -6 = -5.744562647 Reorder the terms: -6 + x = -5.744562647 Solving -6 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.744562647 + 6 x = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 x = 0.255437353 Simplifying x = 0.255437353Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.744562647, 0.255437353}Solution
x = {0, 11.744562647, 0.255437353}
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