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Simplifying 2p2 + 7 = -8p Reorder the terms: 7 + 2p2 = -8p Solving 7 + 2p2 = -8p Solving for variable 'p'. Reorder the terms: 7 + 8p + 2p2 = -8p + 8p Combine like terms: -8p + 8p = 0 7 + 8p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 4p + p2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 4p + -3.5 + p2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 4p + p2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 4p + p2 = 0 + -3.5 4p + p2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 4p + p2 = -3.5 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 = -3.5 + 4 Reorder the terms: 4 + 4p + p2 = -3.5 + 4 Combine like terms: -3.5 + 4 = 0.5 4 + 4p + p2 = 0.5 Factor a perfect square on the left side: (p + 2)(p + 2) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (p + 2) equal to 0.707106781 and -0.707106781.Subproblem 1
p + 2 = 0.707106781 Simplifying p + 2 = 0.707106781 Reorder the terms: 2 + p = 0.707106781 Solving 2 + p = 0.707106781 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 = 0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + p = 0.707106781 + -2 p = 0.707106781 + -2 Combine like terms: 0.707106781 + -2 = -1.292893219 p = -1.292893219 Simplifying p = -1.292893219Subproblem 2
p + 2 = -0.707106781 Simplifying p + 2 = -0.707106781 Reorder the terms: 2 + p = -0.707106781 Solving 2 + p = -0.707106781 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 = -0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + p = -0.707106781 + -2 p = -0.707106781 + -2 Combine like terms: -0.707106781 + -2 = -2.707106781 p = -2.707106781 Simplifying p = -2.707106781Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.292893219, -2.707106781}
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