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Simplifying 4p2 + 8p = 15 Reorder the terms: 8p + 4p2 = 15 Solving 8p + 4p2 = 15 Solving for variable 'p'. Reorder the terms: -15 + 8p + 4p2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 8p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 2p + p2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 2p + 3.75 + p2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 2p + p2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 2p + p2 = 0 + 3.75 2p + p2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 2p + p2 = 3.75 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 = 3.75 + 1 Reorder the terms: 1 + 2p + p2 = 3.75 + 1 Combine like terms: 3.75 + 1 = 4.75 1 + 2p + p2 = 4.75 Factor a perfect square on the left side: (p + 1)(p + 1) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (p + 1) equal to 2.179449472 and -2.179449472.Subproblem 1
p + 1 = 2.179449472 Simplifying p + 1 = 2.179449472 Reorder the terms: 1 + p = 2.179449472 Solving 1 + p = 2.179449472 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 = 2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.179449472 + -1 p = 2.179449472 + -1 Combine like terms: 2.179449472 + -1 = 1.179449472 p = 1.179449472 Simplifying p = 1.179449472Subproblem 2
p + 1 = -2.179449472 Simplifying p + 1 = -2.179449472 Reorder the terms: 1 + p = -2.179449472 Solving 1 + p = -2.179449472 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 = -2.179449472 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.179449472 + -1 p = -2.179449472 + -1 Combine like terms: -2.179449472 + -1 = -3.179449472 p = -3.179449472 Simplifying p = -3.179449472Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.179449472, -3.179449472}
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