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Simplifying 50z5 + 15z4 + 20z3 = 0 Reorder the terms: 20z3 + 15z4 + 50z5 = 0 Solving 20z3 + 15z4 + 50z5 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5z3'. 5z3(4 + 3z + 10z2) = 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 '(4 + 3z + 10z2)' equal to zero and attempt to solve: Simplifying 4 + 3z + 10z2 = 0 Solving 4 + 3z + 10z2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + 0.3z + z2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.3z + -0.4 + z2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.3z + z2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.3z + z2 = 0.0 + -0.4 0.3z + z2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 0.3z + z2 = -0.4 The z term is 0.3z. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3z + 0.0225 + z2 = -0.4 + 0.0225 Reorder the terms: 0.0225 + 0.3z + z2 = -0.4 + 0.0225 Combine like terms: -0.4 + 0.0225 = -0.3775 0.0225 + 0.3z + z2 = -0.3775 Factor a perfect square on the left side: (z + 0.15)(z + 0.15) = -0.3775 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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