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Simplifying 16p6 + -5p4 + -10p2 = 0 Reorder the terms: -10p2 + -5p4 + 16p6 = 0 Solving -10p2 + -5p4 + 16p6 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(-10 + -5p2 + 16p4) = 0Subproblem 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 '(-10 + -5p2 + 16p4)' equal to zero and attempt to solve: Simplifying -10 + -5p2 + 16p4 = 0 Solving -10 + -5p2 + 16p4 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.625 + -0.3125p2 + p4 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.3125p2 + 0.625 + p4 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.3125p2 + p4 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.3125p2 + p4 = 0 + 0.625 -0.3125p2 + p4 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.3125p2 + p4 = 0.625 The p term is -0.3125p2. Take half its coefficient (-0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. -0.3125p2 + 0.0244140625 + p4 = 0.625 + 0.0244140625 Reorder the terms: 0.0244140625 + -0.3125p2 + p4 = 0.625 + 0.0244140625 Combine like terms: 0.625 + 0.0244140625 = 0.6494140625 0.0244140625 + -0.3125p2 + p4 = 0.6494140625 Factor a perfect square on the left side: (p2 + -0.15625)(p2 + -0.15625) = 0.6494140625 Calculate the square root of the right side: 0.80586231 Break this problem into two subproblems by setting (p2 + -0.15625) equal to 0.80586231 and -0.80586231.Subproblem 1
p2 + -0.15625 = 0.80586231 Simplifying p2 + -0.15625 = 0.80586231 Reorder the terms: -0.15625 + p2 = 0.80586231 Solving -0.15625 + p2 = 0.80586231 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + p2 = 0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + p2 = 0.80586231 + 0.15625 p2 = 0.80586231 + 0.15625 Combine like terms: 0.80586231 + 0.15625 = 0.96211231 p2 = 0.96211231 Simplifying p2 = 0.96211231 Take the square root of each side: p = {-0.980873238, 0.980873238}Subproblem 2
p2 + -0.15625 = -0.80586231 Simplifying p2 + -0.15625 = -0.80586231 Reorder the terms: -0.15625 + p2 = -0.80586231 Solving -0.15625 + p2 = -0.80586231 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.15625' to each side of the equation. -0.15625 + 0.15625 + p2 = -0.80586231 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + p2 = -0.80586231 + 0.15625 p2 = -0.80586231 + 0.15625 Combine like terms: -0.80586231 + 0.15625 = -0.64961231 p2 = -0.64961231 Simplifying p2 = -0.64961231 Reorder the terms: 0.64961231 + p2 = -0.64961231 + 0.64961231 Combine like terms: -0.64961231 + 0.64961231 = 0.00000000 0.64961231 + p2 = 0.00000000 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. This subproblem is being ignored because a solution could not be determined.Solution
p = {0}
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