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Simplifying 4p3(4p2 + p + 7) = 0 Reorder the terms: 4p3(7 + p + 4p2) = 0 (7 * 4p3 + p * 4p3 + 4p2 * 4p3) = 0 (28p3 + 4p4 + 16p5) = 0 Solving 28p3 + 4p4 + 16p5 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '4p3'. 4p3(7 + p + 4p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'p3' equal to zero and attempt to solve: Simplifying p3 = 0 Solving p3 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p3 = 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 '(7 + p + 4p2)' equal to zero and attempt to solve: Simplifying 7 + p + 4p2 = 0 Solving 7 + p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + 0.25p + p2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 0.25p + -1.75 + p2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 0.25p + p2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 0.25p + p2 = 0 + -1.75 0.25p + p2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 0.25p + p2 = -1.75 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. 0.25p + 0.25 + p2 = -1.75 + 0.25 Reorder the terms: 0.25 + 0.25p + p2 = -1.75 + 0.25 Combine like terms: -1.75 + 0.25 = -1.5 0.25 + 0.25p + p2 = -1.5 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = -1.5 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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