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Simplifying 8p2 + 16p + -25 = 4 Reorder the terms: -25 + 16p + 8p2 = 4 Solving -25 + 16p + 8p2 = 4 Solving for variable 'p'. Reorder the terms: -25 + -4 + 16p + 8p2 = 4 + -4 Combine like terms: -25 + -4 = -29 -29 + 16p + 8p2 = 4 + -4 Combine like terms: 4 + -4 = 0 -29 + 16p + 8p2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.625 + 2p + p2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 2p + 3.625 + p2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 2p + p2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 2p + p2 = 0 + 3.625 2p + p2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 2p + p2 = 3.625 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 = 3.625 + 1 Reorder the terms: 1 + 2p + p2 = 3.625 + 1 Combine like terms: 3.625 + 1 = 4.625 1 + 2p + p2 = 4.625 Factor a perfect square on the left side: (p + 1)(p + 1) = 4.625 Calculate the square root of the right side: 2.150581317 Break this problem into two subproblems by setting (p + 1) equal to 2.150581317 and -2.150581317.Subproblem 1
p + 1 = 2.150581317 Simplifying p + 1 = 2.150581317 Reorder the terms: 1 + p = 2.150581317 Solving 1 + p = 2.150581317 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 = 2.150581317 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.150581317 + -1 p = 2.150581317 + -1 Combine like terms: 2.150581317 + -1 = 1.150581317 p = 1.150581317 Simplifying p = 1.150581317Subproblem 2
p + 1 = -2.150581317 Simplifying p + 1 = -2.150581317 Reorder the terms: 1 + p = -2.150581317 Solving 1 + p = -2.150581317 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 = -2.150581317 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.150581317 + -1 p = -2.150581317 + -1 Combine like terms: -2.150581317 + -1 = -3.150581317 p = -3.150581317 Simplifying p = -3.150581317Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.150581317, -3.150581317}
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