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Simplifying 3x5 + 11x4 + 20x3 = 0 Reorder the terms: 20x3 + 11x4 + 3x5 = 0 Solving 20x3 + 11x4 + 3x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(20 + 11x + 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 '(20 + 11x + 3x2)' equal to zero and attempt to solve: Simplifying 20 + 11x + 3x2 = 0 Solving 20 + 11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6.666666667 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '-6.666666667' to each side of the equation. 6.666666667 + 3.666666667x + -6.666666667 + x2 = 0 + -6.666666667 Reorder the terms: 6.666666667 + -6.666666667 + 3.666666667x + x2 = 0 + -6.666666667 Combine like terms: 6.666666667 + -6.666666667 = 0.000000000 0.000000000 + 3.666666667x + x2 = 0 + -6.666666667 3.666666667x + x2 = 0 + -6.666666667 Combine like terms: 0 + -6.666666667 = -6.666666667 3.666666667x + x2 = -6.666666667 The x term is 3.666666667x. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667x + 3.361111114 + x2 = -6.666666667 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = -6.666666667 + 3.361111114 Combine like terms: -6.666666667 + 3.361111114 = -3.305555553 3.361111114 + 3.666666667x + x2 = -3.305555553 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = -3.305555553 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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