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Simplifying p2 + -20p + 49 = 0 Reorder the terms: 49 + -20p + p2 = 0 Solving 49 + -20p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -20p + -49 + p2 = 0 + -49 Reorder the terms: 49 + -49 + -20p + p2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -20p + p2 = 0 + -49 -20p + p2 = 0 + -49 Combine like terms: 0 + -49 = -49 -20p + p2 = -49 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 = -49 + 100 Reorder the terms: 100 + -20p + p2 = -49 + 100 Combine like terms: -49 + 100 = 51 100 + -20p + p2 = 51 Factor a perfect square on the left side: (p + -10)(p + -10) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (p + -10) equal to 7.141428429 and -7.141428429.Subproblem 1
p + -10 = 7.141428429 Simplifying p + -10 = 7.141428429 Reorder the terms: -10 + p = 7.141428429 Solving -10 + p = 7.141428429 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 = 7.141428429 + 10 Combine like terms: -10 + 10 = 0 0 + p = 7.141428429 + 10 p = 7.141428429 + 10 Combine like terms: 7.141428429 + 10 = 17.141428429 p = 17.141428429 Simplifying p = 17.141428429Subproblem 2
p + -10 = -7.141428429 Simplifying p + -10 = -7.141428429 Reorder the terms: -10 + p = -7.141428429 Solving -10 + p = -7.141428429 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 = -7.141428429 + 10 Combine like terms: -10 + 10 = 0 0 + p = -7.141428429 + 10 p = -7.141428429 + 10 Combine like terms: -7.141428429 + 10 = 2.858571571 p = 2.858571571 Simplifying p = 2.858571571Solution
The solution to the problem is based on the solutions from the subproblems. p = {17.141428429, 2.858571571}
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