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Simplifying 39x3 + 75x2 + 54x = 16x3 + 38x2 + 12x Reorder the terms: 54x + 75x2 + 39x3 = 16x3 + 38x2 + 12x Reorder the terms: 54x + 75x2 + 39x3 = 12x + 38x2 + 16x3 Solving 54x + 75x2 + 39x3 = 12x + 38x2 + 16x3 Solving for variable 'x'. Reorder the terms: 54x + -12x + 75x2 + -38x2 + 39x3 + -16x3 = 12x + 38x2 + 16x3 + -12x + -38x2 + -16x3 Combine like terms: 54x + -12x = 42x 42x + 75x2 + -38x2 + 39x3 + -16x3 = 12x + 38x2 + 16x3 + -12x + -38x2 + -16x3 Combine like terms: 75x2 + -38x2 = 37x2 42x + 37x2 + 39x3 + -16x3 = 12x + 38x2 + 16x3 + -12x + -38x2 + -16x3 Combine like terms: 39x3 + -16x3 = 23x3 42x + 37x2 + 23x3 = 12x + 38x2 + 16x3 + -12x + -38x2 + -16x3 Reorder the terms: 42x + 37x2 + 23x3 = 12x + -12x + 38x2 + -38x2 + 16x3 + -16x3 Combine like terms: 12x + -12x = 0 42x + 37x2 + 23x3 = 0 + 38x2 + -38x2 + 16x3 + -16x3 42x + 37x2 + 23x3 = 38x2 + -38x2 + 16x3 + -16x3 Combine like terms: 38x2 + -38x2 = 0 42x + 37x2 + 23x3 = 0 + 16x3 + -16x3 42x + 37x2 + 23x3 = 16x3 + -16x3 Combine like terms: 16x3 + -16x3 = 0 42x + 37x2 + 23x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(42 + 37x + 23x2) = 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 '(42 + 37x + 23x2)' equal to zero and attempt to solve: Simplifying 42 + 37x + 23x2 = 0 Solving 42 + 37x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 1.826086957 + 1.608695652x + x2 = 0 Move the constant term to the right: Add '-1.826086957' to each side of the equation. 1.826086957 + 1.608695652x + -1.826086957 + x2 = 0 + -1.826086957 Reorder the terms: 1.826086957 + -1.826086957 + 1.608695652x + x2 = 0 + -1.826086957 Combine like terms: 1.826086957 + -1.826086957 = 0.000000000 0.000000000 + 1.608695652x + x2 = 0 + -1.826086957 1.608695652x + x2 = 0 + -1.826086957 Combine like terms: 0 + -1.826086957 = -1.826086957 1.608695652x + x2 = -1.826086957 The x term is 1.608695652x. Take half its coefficient (0.804347826). Square it (0.6469754252) and add it to both sides. Add '0.6469754252' to each side of the equation. 1.608695652x + 0.6469754252 + x2 = -1.826086957 + 0.6469754252 Reorder the terms: 0.6469754252 + 1.608695652x + x2 = -1.826086957 + 0.6469754252 Combine like terms: -1.826086957 + 0.6469754252 = -1.1791115318 0.6469754252 + 1.608695652x + x2 = -1.1791115318 Factor a perfect square on the left side: (x + 0.804347826)(x + 0.804347826) = -1.1791115318 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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