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Simplifying 30z5 + 35z4 + 25z3 = 0 Reorder the terms: 25z3 + 35z4 + 30z5 = 0 Solving 25z3 + 35z4 + 30z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z3'. 5z3(5 + 7z + 6z2) = 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 + 7z + 6z2)' equal to zero and attempt to solve: Simplifying 5 + 7z + 6z2 = 0 Solving 5 + 7z + 6z2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 1.166666667z + z2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 1.166666667z + -0.8333333333 + z2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 1.166666667z + z2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 1.166666667z + z2 = 0 + -0.8333333333 1.166666667z + z2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 1.166666667z + z2 = -0.8333333333 The z term is 1.166666667z. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667z + 0.3402777780 + z2 = -0.8333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667z + z2 = -0.8333333333 + 0.3402777780 Combine like terms: -0.8333333333 + 0.3402777780 = -0.4930555553 0.3402777780 + 1.166666667z + z2 = -0.4930555553 Factor a perfect square on the left side: (z + 0.5833333335)(z + 0.5833333335) = -0.4930555553 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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