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Simplifying p2 + 4p = 31 Reorder the terms: 4p + p2 = 31 Solving 4p + p2 = 31 Solving for variable 'p'. Reorder the terms: -31 + 4p + p2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 4p + 31 + p2 = 0 + 31 Reorder the terms: -31 + 31 + 4p + p2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 4p + p2 = 0 + 31 4p + p2 = 0 + 31 Combine like terms: 0 + 31 = 31 4p + p2 = 31 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 = 31 + 4 Reorder the terms: 4 + 4p + p2 = 31 + 4 Combine like terms: 31 + 4 = 35 4 + 4p + p2 = 35 Factor a perfect square on the left side: (p + 2)(p + 2) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (p + 2) equal to 5.916079783 and -5.916079783.Subproblem 1
p + 2 = 5.916079783 Simplifying p + 2 = 5.916079783 Reorder the terms: 2 + p = 5.916079783 Solving 2 + p = 5.916079783 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 = 5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + p = 5.916079783 + -2 p = 5.916079783 + -2 Combine like terms: 5.916079783 + -2 = 3.916079783 p = 3.916079783 Simplifying p = 3.916079783Subproblem 2
p + 2 = -5.916079783 Simplifying p + 2 = -5.916079783 Reorder the terms: 2 + p = -5.916079783 Solving 2 + p = -5.916079783 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 = -5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + p = -5.916079783 + -2 p = -5.916079783 + -2 Combine like terms: -5.916079783 + -2 = -7.916079783 p = -7.916079783 Simplifying p = -7.916079783Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.916079783, -7.916079783}
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