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Simplifying p2 + 20p + 88 = 0 Reorder the terms: 88 + 20p + p2 = 0 Solving 88 + 20p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-88' to each side of the equation. 88 + 20p + -88 + p2 = 0 + -88 Reorder the terms: 88 + -88 + 20p + p2 = 0 + -88 Combine like terms: 88 + -88 = 0 0 + 20p + p2 = 0 + -88 20p + p2 = 0 + -88 Combine like terms: 0 + -88 = -88 20p + p2 = -88 The p term is 20p. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20p + 100 + p2 = -88 + 100 Reorder the terms: 100 + 20p + p2 = -88 + 100 Combine like terms: -88 + 100 = 12 100 + 20p + p2 = 12 Factor a perfect square on the left side: (p + 10)(p + 10) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + 10) equal to 3.464101615 and -3.464101615.Subproblem 1
p + 10 = 3.464101615 Simplifying p + 10 = 3.464101615 Reorder the terms: 10 + p = 3.464101615 Solving 10 + p = 3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = 3.464101615 + -10 Combine like terms: 10 + -10 = 0 0 + p = 3.464101615 + -10 p = 3.464101615 + -10 Combine like terms: 3.464101615 + -10 = -6.535898385 p = -6.535898385 Simplifying p = -6.535898385Subproblem 2
p + 10 = -3.464101615 Simplifying p + 10 = -3.464101615 Reorder the terms: 10 + p = -3.464101615 Solving 10 + p = -3.464101615 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + p = -3.464101615 + -10 Combine like terms: 10 + -10 = 0 0 + p = -3.464101615 + -10 p = -3.464101615 + -10 Combine like terms: -3.464101615 + -10 = -13.464101615 p = -13.464101615 Simplifying p = -13.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {-6.535898385, -13.464101615}
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