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Simplifying 2p2 = 7 + 2p Solving 2p2 = 7 + 2p Solving for variable 'p'. Reorder the terms: -7 + -2p + 2p2 = 7 + 2p + -7 + -2p Reorder the terms: -7 + -2p + 2p2 = 7 + -7 + 2p + -2p Combine like terms: 7 + -7 = 0 -7 + -2p + 2p2 = 0 + 2p + -2p -7 + -2p + 2p2 = 2p + -2p Combine like terms: 2p + -2p = 0 -7 + -2p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -1p + p2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -1p + 3.5 + p2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -1p + p2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -1p + p2 = 0 + 3.5 -1p + p2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -1p + p2 = 3.5 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 3.5 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 3.5 + 0.25 Combine like terms: 3.5 + 0.25 = 3.75 0.25 + -1p + p2 = 3.75 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (p + -0.5) equal to 1.936491673 and -1.936491673.Subproblem 1
p + -0.5 = 1.936491673 Simplifying p + -0.5 = 1.936491673 Reorder the terms: -0.5 + p = 1.936491673 Solving -0.5 + p = 1.936491673 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 1.936491673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.936491673 + 0.5 p = 1.936491673 + 0.5 Combine like terms: 1.936491673 + 0.5 = 2.436491673 p = 2.436491673 Simplifying p = 2.436491673Subproblem 2
p + -0.5 = -1.936491673 Simplifying p + -0.5 = -1.936491673 Reorder the terms: -0.5 + p = -1.936491673 Solving -0.5 + p = -1.936491673 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -1.936491673 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.936491673 + 0.5 p = -1.936491673 + 0.5 Combine like terms: -1.936491673 + 0.5 = -1.436491673 p = -1.436491673 Simplifying p = -1.436491673Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.436491673, -1.436491673}
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