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Simplifying (3p2 + -2p + 3) + -1(p2 + -7p + 7) = 0 Reorder the terms: (3 + -2p + 3p2) + -1(p2 + -7p + 7) = 0 Remove parenthesis around (3 + -2p + 3p2) 3 + -2p + 3p2 + -1(p2 + -7p + 7) = 0 Reorder the terms: 3 + -2p + 3p2 + -1(7 + -7p + p2) = 0 3 + -2p + 3p2 + (7 * -1 + -7p * -1 + p2 * -1) = 0 3 + -2p + 3p2 + (-7 + 7p + -1p2) = 0 Reorder the terms: 3 + -7 + -2p + 7p + 3p2 + -1p2 = 0 Combine like terms: 3 + -7 = -4 -4 + -2p + 7p + 3p2 + -1p2 = 0 Combine like terms: -2p + 7p = 5p -4 + 5p + 3p2 + -1p2 = 0 Combine like terms: 3p2 + -1p2 = 2p2 -4 + 5p + 2p2 = 0 Solving -4 + 5p + 2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 2.5p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.5p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 2.5p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.5p + p2 = 0 + 2 2.5p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.5p + p2 = 2 The p term is 2.5p. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5p + 1.5625 + p2 = 2 + 1.5625 Reorder the terms: 1.5625 + 2.5p + p2 = 2 + 1.5625 Combine like terms: 2 + 1.5625 = 3.5625 1.5625 + 2.5p + p2 = 3.5625 Factor a perfect square on the left side: (p + 1.25)(p + 1.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (p + 1.25) equal to 1.887458609 and -1.887458609.Subproblem 1
p + 1.25 = 1.887458609 Simplifying p + 1.25 = 1.887458609 Reorder the terms: 1.25 + p = 1.887458609 Solving 1.25 + p = 1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + p = 1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + p = 1.887458609 + -1.25 p = 1.887458609 + -1.25 Combine like terms: 1.887458609 + -1.25 = 0.637458609 p = 0.637458609 Simplifying p = 0.637458609Subproblem 2
p + 1.25 = -1.887458609 Simplifying p + 1.25 = -1.887458609 Reorder the terms: 1.25 + p = -1.887458609 Solving 1.25 + p = -1.887458609 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + p = -1.887458609 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + p = -1.887458609 + -1.25 p = -1.887458609 + -1.25 Combine like terms: -1.887458609 + -1.25 = -3.137458609 p = -3.137458609 Simplifying p = -3.137458609Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.637458609, -3.137458609}
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