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Simplifying 2p2 + 16p + -1 = 0 Reorder the terms: -1 + 16p + 2p2 = 0 Solving -1 + 16p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 8p + p2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 8p + 0.5 + p2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 8p + p2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 8p + p2 = 0 + 0.5 8p + p2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 8p + p2 = 0.5 The p term is 8p. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8p + 16 + p2 = 0.5 + 16 Reorder the terms: 16 + 8p + p2 = 0.5 + 16 Combine like terms: 0.5 + 16 = 16.5 16 + 8p + p2 = 16.5 Factor a perfect square on the left side: (p + 4)(p + 4) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (p + 4) equal to 4.062019202 and -4.062019202.Subproblem 1
p + 4 = 4.062019202 Simplifying p + 4 = 4.062019202 Reorder the terms: 4 + p = 4.062019202 Solving 4 + p = 4.062019202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = 4.062019202 + -4 Combine like terms: 4 + -4 = 0 0 + p = 4.062019202 + -4 p = 4.062019202 + -4 Combine like terms: 4.062019202 + -4 = 0.062019202 p = 0.062019202 Simplifying p = 0.062019202Subproblem 2
p + 4 = -4.062019202 Simplifying p + 4 = -4.062019202 Reorder the terms: 4 + p = -4.062019202 Solving 4 + p = -4.062019202 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + p = -4.062019202 + -4 Combine like terms: 4 + -4 = 0 0 + p = -4.062019202 + -4 p = -4.062019202 + -4 Combine like terms: -4.062019202 + -4 = -8.062019202 p = -8.062019202 Simplifying p = -8.062019202Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.062019202, -8.062019202}
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