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Simplifying p2 + 20p + -71 = 5 Reorder the terms: -71 + 20p + p2 = 5 Solving -71 + 20p + p2 = 5 Solving for variable 'p'. Reorder the terms: -71 + -5 + 20p + p2 = 5 + -5 Combine like terms: -71 + -5 = -76 -76 + 20p + p2 = 5 + -5 Combine like terms: 5 + -5 = 0 -76 + 20p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 20p + 76 + p2 = 0 + 76 Reorder the terms: -76 + 76 + 20p + p2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 20p + p2 = 0 + 76 20p + p2 = 0 + 76 Combine like terms: 0 + 76 = 76 20p + p2 = 76 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 = 76 + 100 Reorder the terms: 100 + 20p + p2 = 76 + 100 Combine like terms: 76 + 100 = 176 100 + 20p + p2 = 176 Factor a perfect square on the left side: (p + 10)(p + 10) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (p + 10) equal to 13.266499161 and -13.266499161.Subproblem 1
p + 10 = 13.266499161 Simplifying p + 10 = 13.266499161 Reorder the terms: 10 + p = 13.266499161 Solving 10 + p = 13.266499161 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 = 13.266499161 + -10 Combine like terms: 10 + -10 = 0 0 + p = 13.266499161 + -10 p = 13.266499161 + -10 Combine like terms: 13.266499161 + -10 = 3.266499161 p = 3.266499161 Simplifying p = 3.266499161Subproblem 2
p + 10 = -13.266499161 Simplifying p + 10 = -13.266499161 Reorder the terms: 10 + p = -13.266499161 Solving 10 + p = -13.266499161 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 = -13.266499161 + -10 Combine like terms: 10 + -10 = 0 0 + p = -13.266499161 + -10 p = -13.266499161 + -10 Combine like terms: -13.266499161 + -10 = -23.266499161 p = -23.266499161 Simplifying p = -23.266499161Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.266499161, -23.266499161}
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