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Simplifying 21z5 + 15z4 + 9z3 = 0 Reorder the terms: 9z3 + 15z4 + 21z5 = 0 Solving 9z3 + 15z4 + 21z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '3z3'. 3z3(3 + 5z + 7z2) = 0 Ignore the factor 3.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 '(3 + 5z + 7z2)' equal to zero and attempt to solve: Simplifying 3 + 5z + 7z2 = 0 Solving 3 + 5z + 7z2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 0.7142857143z + z2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 0.7142857143z + -0.4285714286 + z2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 0.7142857143z + z2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 0.7142857143z + z2 = 0 + -0.4285714286 0.7142857143z + z2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 0.7142857143z + z2 = -0.4285714286 The z term is 0.7142857143z. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143z + 0.1275510204 + z2 = -0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143z + z2 = -0.4285714286 + 0.1275510204 Combine like terms: -0.4285714286 + 0.1275510204 = -0.3010204082 0.1275510204 + 0.7142857143z + z2 = -0.3010204082 Factor a perfect square on the left side: (z + 0.3571428572)(z + 0.3571428572) = -0.3010204082 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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