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Simplifying 48z5 + 20z4 + 8z3 = 0 Reorder the terms: 8z3 + 20z4 + 48z5 = 0 Solving 8z3 + 20z4 + 48z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '4z3'. 4z3(2 + 5z + 12z2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'z3' equal to zero and attempt to solve: Simplifying z3 = 0 Solving z3 = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z3 = 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 + 5z + 12z2)' equal to zero and attempt to solve: Simplifying 2 + 5z + 12z2 = 0 Solving 2 + 5z + 12z2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + 0.4166666667z + z2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.4166666667z + -0.1666666667 + z2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.4166666667z + z2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.4166666667z + z2 = 0 + -0.1666666667 0.4166666667z + z2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.4166666667z + z2 = -0.1666666667 The z term is 0.4166666667z. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667z + 0.04340277781 + z2 = -0.1666666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667z + z2 = -0.1666666667 + 0.04340277781 Combine like terms: -0.1666666667 + 0.04340277781 = -0.12326388889 0.04340277781 + 0.4166666667z + z2 = -0.12326388889 Factor a perfect square on the left side: (z + 0.2083333334)(z + 0.2083333334) = -0.12326388889 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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