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Simplifying -20p3z + -35p2z + -30pz = 0 Reorder the terms: -30pz + -35p2z + -20p3z = 0 Solving -30pz + -35p2z + -20p3z = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-5pz'. -5pz(6 + 7p + 4p2) = 0 Ignore the factor -5.Subproblem 1
Set the factor 'pz' equal to zero and attempt to solve: Simplifying pz = 0 Solving pz = 0 Move all terms containing p to the left, all other terms to the right. Simplifying pz = 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 '(6 + 7p + 4p2)' equal to zero and attempt to solve: Simplifying 6 + 7p + 4p2 = 0 Solving 6 + 7p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + 1.75p + p2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.75p + -1.5 + p2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.75p + p2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.75p + p2 = 0 + -1.5 1.75p + p2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.75p + p2 = -1.5 The p term is 1.75p. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75p + 0.765625 + p2 = -1.5 + 0.765625 Reorder the terms: 0.765625 + 1.75p + p2 = -1.5 + 0.765625 Combine like terms: -1.5 + 0.765625 = -0.734375 0.765625 + 1.75p + p2 = -0.734375 Factor a perfect square on the left side: (p + 0.875)(p + 0.875) = -0.734375 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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