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Simplifying 42p4t + 30p3t + 42p2t = 0 Reorder the terms: 42p2t + 30p3t + 42p4t = 0 Solving 42p2t + 30p3t + 42p4t = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '6p2t'. 6p2t(7 + 5p + 7p2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'p2t' equal to zero and attempt to solve: Simplifying p2t = 0 Solving p2t = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2t = 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 + 5p + 7p2)' equal to zero and attempt to solve: Simplifying 7 + 5p + 7p2 = 0 Solving 7 + 5p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + 0.7142857143p + p2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.7142857143p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + 0.7142857143p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.7142857143p + p2 = 0 + -1 0.7142857143p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.7142857143p + p2 = -1 The p term is 0.7142857143p. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143p + 0.1275510204 + p2 = -1 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143p + p2 = -1 + 0.1275510204 Combine like terms: -1 + 0.1275510204 = -0.8724489796 0.1275510204 + 0.7142857143p + p2 = -0.8724489796 Factor a perfect square on the left side: (p + 0.3571428572)(p + 0.3571428572) = -0.8724489796 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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