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Simplifying p2 + 2p = 2.25 Reorder the terms: 2p + p2 = 2.25 Solving 2p + p2 = 2.25 Solving for variable 'p'. Reorder the terms: -2.25 + 2p + p2 = 2.25 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + 2p + p2 = 0.00 Begin completing the square. Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2p + 2.25 + p2 = 0.00 + 2.25 Reorder the terms: -2.25 + 2.25 + 2p + p2 = 0.00 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2p + p2 = 0.00 + 2.25 2p + p2 = 0.00 + 2.25 Combine like terms: 0.00 + 2.25 = 2.25 2p + p2 = 2.25 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 = 2.25 + 1 Reorder the terms: 1 + 2p + p2 = 2.25 + 1 Combine like terms: 2.25 + 1 = 3.25 1 + 2p + p2 = 3.25 Factor a perfect square on the left side: (p + 1)(p + 1) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (p + 1) equal to 1.802775638 and -1.802775638.Subproblem 1
p + 1 = 1.802775638 Simplifying p + 1 = 1.802775638 Reorder the terms: 1 + p = 1.802775638 Solving 1 + p = 1.802775638 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 = 1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.802775638 + -1 p = 1.802775638 + -1 Combine like terms: 1.802775638 + -1 = 0.802775638 p = 0.802775638 Simplifying p = 0.802775638Subproblem 2
p + 1 = -1.802775638 Simplifying p + 1 = -1.802775638 Reorder the terms: 1 + p = -1.802775638 Solving 1 + p = -1.802775638 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 = -1.802775638 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.802775638 + -1 p = -1.802775638 + -1 Combine like terms: -1.802775638 + -1 = -2.802775638 p = -2.802775638 Simplifying p = -2.802775638Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.802775638, -2.802775638}
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