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Simplifying 12x6 + 27x5 + 60x4 = 0 Reorder the terms: 60x4 + 27x5 + 12x6 = 0 Solving 60x4 + 27x5 + 12x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x4'. 3x4(20 + 9x + 4x2) = 0 Ignore the factor 3.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 '(20 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying 20 + 9x + 4x2 = 0 Solving 20 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + 2.25x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 2.25x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 2.25x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2.25x + x2 = 0 + -5 2.25x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 2.25x + x2 = -5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -5 + 1.265625 Combine like terms: -5 + 1.265625 = -3.734375 1.265625 + 2.25x + x2 = -3.734375 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = -3.734375 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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