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Simplifying p2 + -20p + -59 = 0 Reorder the terms: -59 + -20p + p2 = 0 Solving -59 + -20p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -20p + 59 + p2 = 0 + 59 Reorder the terms: -59 + 59 + -20p + p2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -20p + p2 = 0 + 59 -20p + p2 = 0 + 59 Combine like terms: 0 + 59 = 59 -20p + p2 = 59 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 = 59 + 100 Reorder the terms: 100 + -20p + p2 = 59 + 100 Combine like terms: 59 + 100 = 159 100 + -20p + p2 = 159 Factor a perfect square on the left side: (p + -10)(p + -10) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (p + -10) equal to 12.609520213 and -12.609520213.Subproblem 1
p + -10 = 12.609520213 Simplifying p + -10 = 12.609520213 Reorder the terms: -10 + p = 12.609520213 Solving -10 + p = 12.609520213 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 = 12.609520213 + 10 Combine like terms: -10 + 10 = 0 0 + p = 12.609520213 + 10 p = 12.609520213 + 10 Combine like terms: 12.609520213 + 10 = 22.609520213 p = 22.609520213 Simplifying p = 22.609520213Subproblem 2
p + -10 = -12.609520213 Simplifying p + -10 = -12.609520213 Reorder the terms: -10 + p = -12.609520213 Solving -10 + p = -12.609520213 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 = -12.609520213 + 10 Combine like terms: -10 + 10 = 0 0 + p = -12.609520213 + 10 p = -12.609520213 + 10 Combine like terms: -12.609520213 + 10 = -2.609520213 p = -2.609520213 Simplifying p = -2.609520213Solution
The solution to the problem is based on the solutions from the subproblems. p = {22.609520213, -2.609520213}
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