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Simplifying 60z5 + 55z4 + 25z3 = 0 Reorder the terms: 25z3 + 55z4 + 60z5 = 0 Solving 25z3 + 55z4 + 60z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z3'. 5z3(5 + 11z + 12z2) = 0 Ignore the factor 5.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 '(5 + 11z + 12z2)' equal to zero and attempt to solve: Simplifying 5 + 11z + 12z2 = 0 Solving 5 + 11z + 12z2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 0.9166666667z + z2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 0.9166666667z + -0.4166666667 + z2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 0.9166666667z + z2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 0.9166666667z + z2 = 0 + -0.4166666667 0.9166666667z + z2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 0.9166666667z + z2 = -0.4166666667 The z term is 0.9166666667z. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667z + 0.2100694445 + z2 = -0.4166666667 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667z + z2 = -0.4166666667 + 0.2100694445 Combine like terms: -0.4166666667 + 0.2100694445 = -0.2065972222 0.2100694445 + 0.9166666667z + z2 = -0.2065972222 Factor a perfect square on the left side: (z + 0.4583333334)(z + 0.4583333334) = -0.2065972222 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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