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Simplifying p2 + -6p + 9 = 99 Reorder the terms: 9 + -6p + p2 = 99 Solving 9 + -6p + p2 = 99 Solving for variable 'p'. Reorder the terms: 9 + -99 + -6p + p2 = 99 + -99 Combine like terms: 9 + -99 = -90 -90 + -6p + p2 = 99 + -99 Combine like terms: 99 + -99 = 0 -90 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -6p + 90 + p2 = 0 + 90 Reorder the terms: -90 + 90 + -6p + p2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -6p + p2 = 0 + 90 -6p + p2 = 0 + 90 Combine like terms: 0 + 90 = 90 -6p + p2 = 90 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = 90 + 9 Reorder the terms: 9 + -6p + p2 = 90 + 9 Combine like terms: 90 + 9 = 99 9 + -6p + p2 = 99 Factor a perfect square on the left side: (p + -3)(p + -3) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (p + -3) equal to 9.949874371 and -9.949874371.Subproblem 1
p + -3 = 9.949874371 Simplifying p + -3 = 9.949874371 Reorder the terms: -3 + p = 9.949874371 Solving -3 + p = 9.949874371 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 9.949874371 + 3 Combine like terms: -3 + 3 = 0 0 + p = 9.949874371 + 3 p = 9.949874371 + 3 Combine like terms: 9.949874371 + 3 = 12.949874371 p = 12.949874371 Simplifying p = 12.949874371Subproblem 2
p + -3 = -9.949874371 Simplifying p + -3 = -9.949874371 Reorder the terms: -3 + p = -9.949874371 Solving -3 + p = -9.949874371 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -9.949874371 + 3 Combine like terms: -3 + 3 = 0 0 + p = -9.949874371 + 3 p = -9.949874371 + 3 Combine like terms: -9.949874371 + 3 = -6.949874371 p = -6.949874371 Simplifying p = -6.949874371Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.949874371, -6.949874371}
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