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Simplifying 2p2 + 16p = -2p2 + 3 Reorder the terms: 16p + 2p2 = -2p2 + 3 Reorder the terms: 16p + 2p2 = 3 + -2p2 Solving 16p + 2p2 = 3 + -2p2 Solving for variable 'p'. Reorder the terms: -3 + 16p + 2p2 + 2p2 = 3 + -2p2 + -3 + 2p2 Combine like terms: 2p2 + 2p2 = 4p2 -3 + 16p + 4p2 = 3 + -2p2 + -3 + 2p2 Reorder the terms: -3 + 16p + 4p2 = 3 + -3 + -2p2 + 2p2 Combine like terms: 3 + -3 = 0 -3 + 16p + 4p2 = 0 + -2p2 + 2p2 -3 + 16p + 4p2 = -2p2 + 2p2 Combine like terms: -2p2 + 2p2 = 0 -3 + 16p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 4p + p2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 4p + 0.75 + p2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 4p + p2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 4p + p2 = 0 + 0.75 4p + p2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 4p + p2 = 0.75 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 0.75 + 4 Reorder the terms: 4 + 4p + p2 = 0.75 + 4 Combine like terms: 0.75 + 4 = 4.75 4 + 4p + p2 = 4.75 Factor a perfect square on the left side: (p + 2)(p + 2) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (p + 2) equal to 2.179449472 and -2.179449472.Subproblem 1
p + 2 = 2.179449472 Simplifying p + 2 = 2.179449472 Reorder the terms: 2 + p = 2.179449472 Solving 2 + p = 2.179449472 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + p = 2.179449472 + -2 p = 2.179449472 + -2 Combine like terms: 2.179449472 + -2 = 0.179449472 p = 0.179449472 Simplifying p = 0.179449472Subproblem 2
p + 2 = -2.179449472 Simplifying p + 2 = -2.179449472 Reorder the terms: 2 + p = -2.179449472 Solving 2 + p = -2.179449472 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + p = -2.179449472 + -2 p = -2.179449472 + -2 Combine like terms: -2.179449472 + -2 = -4.179449472 p = -4.179449472 Simplifying p = -4.179449472Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.179449472, -4.179449472}
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