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Simplifying 9 = 60p + -1p2 Solving 9 = 60p + -1p2 Solving for variable 'p'. Reorder the terms: 9 + -60p + p2 = 60p + -60p + -1p2 + p2 Combine like terms: 60p + -60p = 0 9 + -60p + p2 = 0 + -1p2 + p2 9 + -60p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 9 + -60p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -60p + -9 + p2 = 0 + -9 Reorder the terms: 9 + -9 + -60p + p2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -60p + p2 = 0 + -9 -60p + p2 = 0 + -9 Combine like terms: 0 + -9 = -9 -60p + p2 = -9 The p term is -60p. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60p + 900 + p2 = -9 + 900 Reorder the terms: 900 + -60p + p2 = -9 + 900 Combine like terms: -9 + 900 = 891 900 + -60p + p2 = 891 Factor a perfect square on the left side: (p + -30)(p + -30) = 891 Calculate the square root of the right side: 29.849623113 Break this problem into two subproblems by setting (p + -30) equal to 29.849623113 and -29.849623113.Subproblem 1
p + -30 = 29.849623113 Simplifying p + -30 = 29.849623113 Reorder the terms: -30 + p = 29.849623113 Solving -30 + p = 29.849623113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + p = 29.849623113 + 30 Combine like terms: -30 + 30 = 0 0 + p = 29.849623113 + 30 p = 29.849623113 + 30 Combine like terms: 29.849623113 + 30 = 59.849623113 p = 59.849623113 Simplifying p = 59.849623113Subproblem 2
p + -30 = -29.849623113 Simplifying p + -30 = -29.849623113 Reorder the terms: -30 + p = -29.849623113 Solving -30 + p = -29.849623113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + p = -29.849623113 + 30 Combine like terms: -30 + 30 = 0 0 + p = -29.849623113 + 30 p = -29.849623113 + 30 Combine like terms: -29.849623113 + 30 = 0.150376887 p = 0.150376887 Simplifying p = 0.150376887Solution
The solution to the problem is based on the solutions from the subproblems. p = {59.849623113, 0.150376887}
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