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Simplifying (3x3) + (4x2) + (4x) = 0 Reorder the terms: (4x) + (4x2) + (3x3) = 0 Solving (4x) + (4x2) + (3x3) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + (4x) + (3x2)) = 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 '(4 + (4x) + (3x2))' equal to zero and attempt to solve: Simplifying 4 + (4x) + (3x2) = 0 Solving 4 + (4x) + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + (1.333333333x) + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + (1.333333333x) + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + (1.333333333x) + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + (1.333333333x) + x2 = 0 + -1.333333333 (1.333333333x) + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 (1.333333333x) + x2 = -1.333333333 The x term is (1.333333333x). Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. (1.333333333x) + 0.4444444442 + x2 = -1.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + (1.333333333x) + x2 = -1.333333333 + 0.4444444442 Combine like terms: -1.333333333 + 0.4444444442 = -0.8888888888 0.4444444442 + (1.333333333x) + x2 = -0.8888888888 Factor a perfect square on the left side: ((x) + 0.6666666665)((x) + 0.6666666665) = -0.8888888888 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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