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Simplifying 32p2 + -8p6 = 0 Solving 32p2 + -8p6 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '8p2'. 8p2(4 + -1p4) = 0 Factor a difference between two squares. 8p2((2 + p2)(2 + -1p2)) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(2 + p2)' equal to zero and attempt to solve: Simplifying 2 + p2 = 0 Solving 2 + p2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + p2 = 0 + -2 p2 = 0 + -2 Combine like terms: 0 + -2 = -2 p2 = -2 Simplifying p2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + -1p2)' equal to zero and attempt to solve: Simplifying 2 + -1p2 = 0 Solving 2 + -1p2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p2 = 0 + -2 -1p2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1p2 = -2 Divide each side by '-1'. p2 = 2 Simplifying p2 = 2 Take the square root of each side: p = {-1.414213562, 1.414213562}Solution
p = {0, -1.414213562, 1.414213562}
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