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Simplifying p2 + 21p + 99 = 0 Reorder the terms: 99 + 21p + p2 = 0 Solving 99 + 21p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-99' to each side of the equation. 99 + 21p + -99 + p2 = 0 + -99 Reorder the terms: 99 + -99 + 21p + p2 = 0 + -99 Combine like terms: 99 + -99 = 0 0 + 21p + p2 = 0 + -99 21p + p2 = 0 + -99 Combine like terms: 0 + -99 = -99 21p + p2 = -99 The p term is 21p. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21p + 110.25 + p2 = -99 + 110.25 Reorder the terms: 110.25 + 21p + p2 = -99 + 110.25 Combine like terms: -99 + 110.25 = 11.25 110.25 + 21p + p2 = 11.25 Factor a perfect square on the left side: (p + 10.5)(p + 10.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (p + 10.5) equal to 3.354101966 and -3.354101966.Subproblem 1
p + 10.5 = 3.354101966 Simplifying p + 10.5 = 3.354101966 Reorder the terms: 10.5 + p = 3.354101966 Solving 10.5 + p = 3.354101966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + p = 3.354101966 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + p = 3.354101966 + -10.5 p = 3.354101966 + -10.5 Combine like terms: 3.354101966 + -10.5 = -7.145898034 p = -7.145898034 Simplifying p = -7.145898034Subproblem 2
p + 10.5 = -3.354101966 Simplifying p + 10.5 = -3.354101966 Reorder the terms: 10.5 + p = -3.354101966 Solving 10.5 + p = -3.354101966 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + p = -3.354101966 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + p = -3.354101966 + -10.5 p = -3.354101966 + -10.5 Combine like terms: -3.354101966 + -10.5 = -13.854101966 p = -13.854101966 Simplifying p = -13.854101966Solution
The solution to the problem is based on the solutions from the subproblems. p = {-7.145898034, -13.854101966}
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