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Simplifying 2p2 + 16p + 13 = 0 Reorder the terms: 13 + 16p + 2p2 = 0 Solving 13 + 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'. 6.5 + 8p + p2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 8p + -6.5 + p2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 8p + p2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 8p + p2 = 0 + -6.5 8p + p2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 8p + p2 = -6.5 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 = -6.5 + 16 Reorder the terms: 16 + 8p + p2 = -6.5 + 16 Combine like terms: -6.5 + 16 = 9.5 16 + 8p + p2 = 9.5 Factor a perfect square on the left side: (p + 4)(p + 4) = 9.5 Calculate the square root of the right side: 3.082207001 Break this problem into two subproblems by setting (p + 4) equal to 3.082207001 and -3.082207001.Subproblem 1
p + 4 = 3.082207001 Simplifying p + 4 = 3.082207001 Reorder the terms: 4 + p = 3.082207001 Solving 4 + p = 3.082207001 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 = 3.082207001 + -4 Combine like terms: 4 + -4 = 0 0 + p = 3.082207001 + -4 p = 3.082207001 + -4 Combine like terms: 3.082207001 + -4 = -0.917792999 p = -0.917792999 Simplifying p = -0.917792999Subproblem 2
p + 4 = -3.082207001 Simplifying p + 4 = -3.082207001 Reorder the terms: 4 + p = -3.082207001 Solving 4 + p = -3.082207001 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 = -3.082207001 + -4 Combine like terms: 4 + -4 = 0 0 + p = -3.082207001 + -4 p = -3.082207001 + -4 Combine like terms: -3.082207001 + -4 = -7.082207001 p = -7.082207001 Simplifying p = -7.082207001Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.917792999, -7.082207001}
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