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Simplifying -12p4y + -2p3y + -4p2y = 0 Reorder the terms: -4p2y + -2p3y + -12p4y = 0 Solving -4p2y + -2p3y + -12p4y = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '-2p2y'. -2p2y(2 + p + 6p2) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'p2y' equal to zero and attempt to solve: Simplifying p2y = 0 Solving p2y = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2y = 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 '(2 + p + 6p2)' equal to zero and attempt to solve: Simplifying 2 + p + 6p2 = 0 Solving 2 + p + 6p2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.3333333333 + 0.1666666667p + p2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.1666666667p + -0.3333333333 + p2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.1666666667p + p2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.1666666667p + p2 = 0 + -0.3333333333 0.1666666667p + p2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.1666666667p + p2 = -0.3333333333 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667p + 0.25 + p2 = -0.3333333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667p + p2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 0.25 + 0.1666666667p + p2 = -0.0833333333 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = -0.0833333333 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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