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Simplifying 40z5 + 30z4 + 25z3 = 0 Reorder the terms: 25z3 + 30z4 + 40z5 = 0 Solving 25z3 + 30z4 + 40z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z3'. 5z3(5 + 6z + 8z2) = 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 + 6z + 8z2)' equal to zero and attempt to solve: Simplifying 5 + 6z + 8z2 = 0 Solving 5 + 6z + 8z2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 0.75z + z2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.75z + -0.625 + z2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.75z + z2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.75z + z2 = 0 + -0.625 0.75z + z2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.75z + z2 = -0.625 The z term is 0.75z. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75z + 0.140625 + z2 = -0.625 + 0.140625 Reorder the terms: 0.140625 + 0.75z + z2 = -0.625 + 0.140625 Combine like terms: -0.625 + 0.140625 = -0.484375 0.140625 + 0.75z + z2 = -0.484375 Factor a perfect square on the left side: (z + 0.375)(z + 0.375) = -0.484375 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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