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Simplifying 12x3 + 4x2 + 1x = 0 Reorder the terms: 1x + 4x2 + 12x3 = 0 Solving 1x + 4x2 + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 4x + 12x2) = 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 '(1 + 4x + 12x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + 12x2 = 0 Solving 1 + 4x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 0.3333333333x + -0.08333333333 + x2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 0.3333333333x + x2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.08333333333 0.3333333333x + x2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 0.3333333333x + x2 = -0.08333333333 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.08333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.08333333333 + 0.02777777779 Combine like terms: -0.08333333333 + 0.02777777779 = -0.05555555554 0.02777777779 + 0.3333333333x + x2 = -0.05555555554 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.05555555554 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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