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Simplifying p2 + -10p + -15 = 0 Reorder the terms: -15 + -10p + p2 = 0 Solving -15 + -10p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -10p + 15 + p2 = 0 + 15 Reorder the terms: -15 + 15 + -10p + p2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -10p + p2 = 0 + 15 -10p + p2 = 0 + 15 Combine like terms: 0 + 15 = 15 -10p + p2 = 15 The p term is -10p. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10p + 25 + p2 = 15 + 25 Reorder the terms: 25 + -10p + p2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + -10p + p2 = 40 Factor a perfect square on the left side: (p + -5)(p + -5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (p + -5) equal to 6.32455532 and -6.32455532.Subproblem 1
p + -5 = 6.32455532 Simplifying p + -5 = 6.32455532 Reorder the terms: -5 + p = 6.32455532 Solving -5 + p = 6.32455532 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = 6.32455532 + 5 Combine like terms: -5 + 5 = 0 0 + p = 6.32455532 + 5 p = 6.32455532 + 5 Combine like terms: 6.32455532 + 5 = 11.32455532 p = 11.32455532 Simplifying p = 11.32455532Subproblem 2
p + -5 = -6.32455532 Simplifying p + -5 = -6.32455532 Reorder the terms: -5 + p = -6.32455532 Solving -5 + p = -6.32455532 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + p = -6.32455532 + 5 Combine like terms: -5 + 5 = 0 0 + p = -6.32455532 + 5 p = -6.32455532 + 5 Combine like terms: -6.32455532 + 5 = -1.32455532 p = -1.32455532 Simplifying p = -1.32455532Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.32455532, -1.32455532}
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