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Simplifying p2 + -2p + -44 = -7 Reorder the terms: -44 + -2p + p2 = -7 Solving -44 + -2p + p2 = -7 Solving for variable 'p'. Reorder the terms: -44 + 7 + -2p + p2 = -7 + 7 Combine like terms: -44 + 7 = -37 -37 + -2p + p2 = -7 + 7 Combine like terms: -7 + 7 = 0 -37 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -2p + 37 + p2 = 0 + 37 Reorder the terms: -37 + 37 + -2p + p2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -2p + p2 = 0 + 37 -2p + p2 = 0 + 37 Combine like terms: 0 + 37 = 37 -2p + p2 = 37 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 = 37 + 1 Reorder the terms: 1 + -2p + p2 = 37 + 1 Combine like terms: 37 + 1 = 38 1 + -2p + p2 = 38 Factor a perfect square on the left side: (p + -1)(p + -1) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (p + -1) equal to 6.164414003 and -6.164414003.Subproblem 1
p + -1 = 6.164414003 Simplifying p + -1 = 6.164414003 Reorder the terms: -1 + p = 6.164414003 Solving -1 + p = 6.164414003 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 = 6.164414003 + 1 Combine like terms: -1 + 1 = 0 0 + p = 6.164414003 + 1 p = 6.164414003 + 1 Combine like terms: 6.164414003 + 1 = 7.164414003 p = 7.164414003 Simplifying p = 7.164414003Subproblem 2
p + -1 = -6.164414003 Simplifying p + -1 = -6.164414003 Reorder the terms: -1 + p = -6.164414003 Solving -1 + p = -6.164414003 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 = -6.164414003 + 1 Combine like terms: -1 + 1 = 0 0 + p = -6.164414003 + 1 p = -6.164414003 + 1 Combine like terms: -6.164414003 + 1 = -5.164414003 p = -5.164414003 Simplifying p = -5.164414003Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.164414003, -5.164414003}
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