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Simplifying 12x6 + 16x5 + 8x4 = 0 Reorder the terms: 8x4 + 16x5 + 12x6 = 0 Solving 8x4 + 16x5 + 12x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x4'. 4x4(2 + 4x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + 3x2 = 0 Solving 2 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + 1.333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + 1.333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.6666666667 1.333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 1.333333333x + x2 = -0.6666666667 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 = -0.6666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.6666666667 + 0.4444444442 Combine like terms: -0.6666666667 + 0.4444444442 = -0.2222222225 0.4444444442 + 1.333333333x + x2 = -0.2222222225 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -0.2222222225 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. The solution to this equation could not be determined.
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