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Simplifying p2 + -8p + -39 = -10 Reorder the terms: -39 + -8p + p2 = -10 Solving -39 + -8p + p2 = -10 Solving for variable 'p'. Reorder the terms: -39 + 10 + -8p + p2 = -10 + 10 Combine like terms: -39 + 10 = -29 -29 + -8p + p2 = -10 + 10 Combine like terms: -10 + 10 = 0 -29 + -8p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -8p + 29 + p2 = 0 + 29 Reorder the terms: -29 + 29 + -8p + p2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -8p + p2 = 0 + 29 -8p + p2 = 0 + 29 Combine like terms: 0 + 29 = 29 -8p + p2 = 29 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 29 + 16 Reorder the terms: 16 + -8p + p2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + -8p + p2 = 45 Factor a perfect square on the left side: (p + -4)(p + -4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (p + -4) equal to 6.708203933 and -6.708203933.Subproblem 1
p + -4 = 6.708203933 Simplifying p + -4 = 6.708203933 Reorder the terms: -4 + p = 6.708203933 Solving -4 + p = 6.708203933 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 6.708203933 + 4 Combine like terms: -4 + 4 = 0 0 + p = 6.708203933 + 4 p = 6.708203933 + 4 Combine like terms: 6.708203933 + 4 = 10.708203933 p = 10.708203933 Simplifying p = 10.708203933Subproblem 2
p + -4 = -6.708203933 Simplifying p + -4 = -6.708203933 Reorder the terms: -4 + p = -6.708203933 Solving -4 + p = -6.708203933 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -6.708203933 + 4 Combine like terms: -4 + 4 = 0 0 + p = -6.708203933 + 4 p = -6.708203933 + 4 Combine like terms: -6.708203933 + 4 = -2.708203933 p = -2.708203933 Simplifying p = -2.708203933Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.708203933, -2.708203933}
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