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Simplifying p2 + -9p + -45 = 0 Reorder the terms: -45 + -9p + p2 = 0 Solving -45 + -9p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -9p + 45 + p2 = 0 + 45 Reorder the terms: -45 + 45 + -9p + p2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -9p + p2 = 0 + 45 -9p + p2 = 0 + 45 Combine like terms: 0 + 45 = 45 -9p + p2 = 45 The p term is -9p. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9p + 20.25 + p2 = 45 + 20.25 Reorder the terms: 20.25 + -9p + p2 = 45 + 20.25 Combine like terms: 45 + 20.25 = 65.25 20.25 + -9p + p2 = 65.25 Factor a perfect square on the left side: (p + -4.5)(p + -4.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (p + -4.5) equal to 8.077747211 and -8.077747211.Subproblem 1
p + -4.5 = 8.077747211 Simplifying p + -4.5 = 8.077747211 Reorder the terms: -4.5 + p = 8.077747211 Solving -4.5 + p = 8.077747211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = 8.077747211 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = 8.077747211 + 4.5 p = 8.077747211 + 4.5 Combine like terms: 8.077747211 + 4.5 = 12.577747211 p = 12.577747211 Simplifying p = 12.577747211Subproblem 2
p + -4.5 = -8.077747211 Simplifying p + -4.5 = -8.077747211 Reorder the terms: -4.5 + p = -8.077747211 Solving -4.5 + p = -8.077747211 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + p = -8.077747211 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + p = -8.077747211 + 4.5 p = -8.077747211 + 4.5 Combine like terms: -8.077747211 + 4.5 = -3.577747211 p = -3.577747211 Simplifying p = -3.577747211Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.577747211, -3.577747211}
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