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Simplifying 3x5 + 1x4 + 27x3 = 0 Reorder the terms: 27x3 + 1x4 + 3x5 = 0 Solving 27x3 + 1x4 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(27 + x + 3x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 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 '(27 + x + 3x2)' equal to zero and attempt to solve: Simplifying 27 + x + 3x2 = 0 Solving 27 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 0.3333333333x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 0.3333333333x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 0.3333333333x + x2 = 0 + -9 0.3333333333x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 0.3333333333x + x2 = -9 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -9 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -9 + 0.25 Combine like terms: -9 + 0.25 = -8.75 0.25 + 0.3333333333x + x2 = -8.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -8.75 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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