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Simplifying p2 + 4p + 4 = 40 Reorder the terms: 4 + 4p + p2 = 40 Solving 4 + 4p + p2 = 40 Solving for variable 'p'. Reorder the terms: 4 + -40 + 4p + p2 = 40 + -40 Combine like terms: 4 + -40 = -36 -36 + 4p + p2 = 40 + -40 Combine like terms: 40 + -40 = 0 -36 + 4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 4p + 36 + p2 = 0 + 36 Reorder the terms: -36 + 36 + 4p + p2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4p + p2 = 0 + 36 4p + p2 = 0 + 36 Combine like terms: 0 + 36 = 36 4p + p2 = 36 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 = 36 + 4 Reorder the terms: 4 + 4p + p2 = 36 + 4 Combine like terms: 36 + 4 = 40 4 + 4p + p2 = 40 Factor a perfect square on the left side: (p + 2)(p + 2) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (p + 2) equal to 6.32455532 and -6.32455532.Subproblem 1
p + 2 = 6.32455532 Simplifying p + 2 = 6.32455532 Reorder the terms: 2 + p = 6.32455532 Solving 2 + p = 6.32455532 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 = 6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + p = 6.32455532 + -2 p = 6.32455532 + -2 Combine like terms: 6.32455532 + -2 = 4.32455532 p = 4.32455532 Simplifying p = 4.32455532Subproblem 2
p + 2 = -6.32455532 Simplifying p + 2 = -6.32455532 Reorder the terms: 2 + p = -6.32455532 Solving 2 + p = -6.32455532 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 = -6.32455532 + -2 Combine like terms: 2 + -2 = 0 0 + p = -6.32455532 + -2 p = -6.32455532 + -2 Combine like terms: -6.32455532 + -2 = -8.32455532 p = -8.32455532 Simplifying p = -8.32455532Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.32455532, -8.32455532}
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