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Simplifying p2 + 22p + -9 = 0 Reorder the terms: -9 + 22p + p2 = 0 Solving -9 + 22p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 22p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + 22p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 22p + p2 = 0 + 9 22p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 22p + p2 = 9 The p term is 22p. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22p + 121 + p2 = 9 + 121 Reorder the terms: 121 + 22p + p2 = 9 + 121 Combine like terms: 9 + 121 = 130 121 + 22p + p2 = 130 Factor a perfect square on the left side: (p + 11)(p + 11) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (p + 11) equal to 11.401754251 and -11.401754251.Subproblem 1
p + 11 = 11.401754251 Simplifying p + 11 = 11.401754251 Reorder the terms: 11 + p = 11.401754251 Solving 11 + p = 11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = 11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + p = 11.401754251 + -11 p = 11.401754251 + -11 Combine like terms: 11.401754251 + -11 = 0.401754251 p = 0.401754251 Simplifying p = 0.401754251Subproblem 2
p + 11 = -11.401754251 Simplifying p + 11 = -11.401754251 Reorder the terms: 11 + p = -11.401754251 Solving 11 + p = -11.401754251 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + p = -11.401754251 + -11 Combine like terms: 11 + -11 = 0 0 + p = -11.401754251 + -11 p = -11.401754251 + -11 Combine like terms: -11.401754251 + -11 = -22.401754251 p = -22.401754251 Simplifying p = -22.401754251Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.401754251, -22.401754251}
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