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Simplifying 4z3 + -2z2 + 14z = 0 Reorder the terms: 14z + -2z2 + 4z3 = 0 Solving 14z + -2z2 + 4z3 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '2z'. 2z(7 + -1z + 2z2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'z' equal to zero and attempt to solve: Simplifying z = 0 Solving z = 0 Move all terms containing z to the left, all other terms to the right. Simplifying z = 0Subproblem 2
Set the factor '(7 + -1z + 2z2)' equal to zero and attempt to solve: Simplifying 7 + -1z + 2z2 = 0 Solving 7 + -1z + 2z2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -0.5z + z2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -0.5z + -3.5 + z2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -0.5z + z2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -0.5z + z2 = 0 + -3.5 -0.5z + z2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -0.5z + z2 = -3.5 The z term is -0.5z. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5z + 0.0625 + z2 = -3.5 + 0.0625 Reorder the terms: 0.0625 + -0.5z + z2 = -3.5 + 0.0625 Combine like terms: -3.5 + 0.0625 = -3.4375 0.0625 + -0.5z + z2 = -3.4375 Factor a perfect square on the left side: (z + -0.25)(z + -0.25) = -3.4375 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.Solution
z = {0}
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