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Simplifying p2 + 22p = -25 Reorder the terms: 22p + p2 = -25 Solving 22p + p2 = -25 Solving for variable 'p'. Reorder the terms: 25 + 22p + p2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + 22p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 22p + -25 + p2 = 0 + -25 Reorder the terms: 25 + -25 + 22p + p2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 22p + p2 = 0 + -25 22p + p2 = 0 + -25 Combine like terms: 0 + -25 = -25 22p + p2 = -25 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 = -25 + 121 Reorder the terms: 121 + 22p + p2 = -25 + 121 Combine like terms: -25 + 121 = 96 121 + 22p + p2 = 96 Factor a perfect square on the left side: (p + 11)(p + 11) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (p + 11) equal to 9.797958971 and -9.797958971.Subproblem 1
p + 11 = 9.797958971 Simplifying p + 11 = 9.797958971 Reorder the terms: 11 + p = 9.797958971 Solving 11 + p = 9.797958971 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 = 9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + p = 9.797958971 + -11 p = 9.797958971 + -11 Combine like terms: 9.797958971 + -11 = -1.202041029 p = -1.202041029 Simplifying p = -1.202041029Subproblem 2
p + 11 = -9.797958971 Simplifying p + 11 = -9.797958971 Reorder the terms: 11 + p = -9.797958971 Solving 11 + p = -9.797958971 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 = -9.797958971 + -11 Combine like terms: 11 + -11 = 0 0 + p = -9.797958971 + -11 p = -9.797958971 + -11 Combine like terms: -9.797958971 + -11 = -20.797958971 p = -20.797958971 Simplifying p = -20.797958971Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.202041029, -20.797958971}
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