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Simplifying 9p4 + 5 = 46p2 Reorder the terms: 5 + 9p4 = 46p2 Solving 5 + 9p4 = 46p2 Solving for variable 'p'. Reorder the terms: 5 + -46p2 + 9p4 = 46p2 + -46p2 Combine like terms: 46p2 + -46p2 = 0 5 + -46p2 + 9p4 = 0 Factor a trinomial. (1 + -9p2)(5 + -1p2) = 0 Factor a difference between two squares. ((1 + 3p)(1 + -3p))(5 + -1p2) = 0Subproblem 1
Set the factor '(5 + -1p2)' equal to zero and attempt to solve: Simplifying 5 + -1p2 = 0 Solving 5 + -1p2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1p2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p2 = 0 + -5 -1p2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1p2 = -5 Divide each side by '-1'. p2 = 5 Simplifying p2 = 5 Take the square root of each side: p = {-2.236067978, 2.236067978}Subproblem 2
Set the factor '(1 + 3p)' equal to zero and attempt to solve: Simplifying 1 + 3p = 0 Solving 1 + 3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3p = 0 + -1 3p = 0 + -1 Combine like terms: 0 + -1 = -1 3p = -1 Divide each side by '3'. p = -0.3333333333 Simplifying p = -0.3333333333Subproblem 3
Set the factor '(1 + -3p)' equal to zero and attempt to solve: Simplifying 1 + -3p = 0 Solving 1 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3p = 0 + -1 -3p = 0 + -1 Combine like terms: 0 + -1 = -1 -3p = -1 Divide each side by '-3'. p = 0.3333333333 Simplifying p = 0.3333333333Solution
p = {-2.236067978, 2.236067978, -0.3333333333, 0.3333333333}
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