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Simplifying p2 + 18p = 49 Reorder the terms: 18p + p2 = 49 Solving 18p + p2 = 49 Solving for variable 'p'. Reorder the terms: -49 + 18p + p2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + 18p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 18p + 49 + p2 = 0 + 49 Reorder the terms: -49 + 49 + 18p + p2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 18p + p2 = 0 + 49 18p + p2 = 0 + 49 Combine like terms: 0 + 49 = 49 18p + p2 = 49 The p term is 18p. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18p + 81 + p2 = 49 + 81 Reorder the terms: 81 + 18p + p2 = 49 + 81 Combine like terms: 49 + 81 = 130 81 + 18p + p2 = 130 Factor a perfect square on the left side: (p + 9)(p + 9) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (p + 9) equal to 11.401754251 and -11.401754251.Subproblem 1
p + 9 = 11.401754251 Simplifying p + 9 = 11.401754251 Reorder the terms: 9 + p = 11.401754251 Solving 9 + p = 11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = 11.401754251 + -9 Combine like terms: 9 + -9 = 0 0 + p = 11.401754251 + -9 p = 11.401754251 + -9 Combine like terms: 11.401754251 + -9 = 2.401754251 p = 2.401754251 Simplifying p = 2.401754251Subproblem 2
p + 9 = -11.401754251 Simplifying p + 9 = -11.401754251 Reorder the terms: 9 + p = -11.401754251 Solving 9 + p = -11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + p = -11.401754251 + -9 Combine like terms: 9 + -9 = 0 0 + p = -11.401754251 + -9 p = -11.401754251 + -9 Combine like terms: -11.401754251 + -9 = -20.401754251 p = -20.401754251 Simplifying p = -20.401754251Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.401754251, -20.401754251}
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