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Simplifying 8p2 + 16p + -25 = 0 Reorder the terms: -25 + 16p + 8p2 = 0 Solving -25 + 16p + 8p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 2p + p2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 2p + 3.125 + p2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 2p + p2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 2p + p2 = 0 + 3.125 2p + p2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 2p + p2 = 3.125 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 3.125 + 1 Reorder the terms: 1 + 2p + p2 = 3.125 + 1 Combine like terms: 3.125 + 1 = 4.125 1 + 2p + p2 = 4.125 Factor a perfect square on the left side: (p + 1)(p + 1) = 4.125 Calculate the square root of the right side: 2.031009601 Break this problem into two subproblems by setting (p + 1) equal to 2.031009601 and -2.031009601.Subproblem 1
p + 1 = 2.031009601 Simplifying p + 1 = 2.031009601 Reorder the terms: 1 + p = 2.031009601 Solving 1 + p = 2.031009601 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 2.031009601 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.031009601 + -1 p = 2.031009601 + -1 Combine like terms: 2.031009601 + -1 = 1.031009601 p = 1.031009601 Simplifying p = 1.031009601Subproblem 2
p + 1 = -2.031009601 Simplifying p + 1 = -2.031009601 Reorder the terms: 1 + p = -2.031009601 Solving 1 + p = -2.031009601 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -2.031009601 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.031009601 + -1 p = -2.031009601 + -1 Combine like terms: -2.031009601 + -1 = -3.031009601 p = -3.031009601 Simplifying p = -3.031009601Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.031009601, -3.031009601}
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