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Simplifying p2 + 4p + -49 = 0 Reorder the terms: -49 + 4p + p2 = 0 Solving -49 + 4p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 4p + 49 + p2 = 0 + 49 Reorder the terms: -49 + 49 + 4p + p2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 4p + p2 = 0 + 49 4p + p2 = 0 + 49 Combine like terms: 0 + 49 = 49 4p + p2 = 49 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 = 49 + 4 Reorder the terms: 4 + 4p + p2 = 49 + 4 Combine like terms: 49 + 4 = 53 4 + 4p + p2 = 53 Factor a perfect square on the left side: (p + 2)(p + 2) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (p + 2) equal to 7.280109889 and -7.280109889.Subproblem 1
p + 2 = 7.280109889 Simplifying p + 2 = 7.280109889 Reorder the terms: 2 + p = 7.280109889 Solving 2 + p = 7.280109889 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 = 7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + p = 7.280109889 + -2 p = 7.280109889 + -2 Combine like terms: 7.280109889 + -2 = 5.280109889 p = 5.280109889 Simplifying p = 5.280109889Subproblem 2
p + 2 = -7.280109889 Simplifying p + 2 = -7.280109889 Reorder the terms: 2 + p = -7.280109889 Solving 2 + p = -7.280109889 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 = -7.280109889 + -2 Combine like terms: 2 + -2 = 0 0 + p = -7.280109889 + -2 p = -7.280109889 + -2 Combine like terms: -7.280109889 + -2 = -9.280109889 p = -9.280109889 Simplifying p = -9.280109889Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.280109889, -9.280109889}
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