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Simplifying p2 + -20p + -5 = 0 Reorder the terms: -5 + -20p + p2 = 0 Solving -5 + -20p + p2 = 0 Solving for variable 'p'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -20p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + -20p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -20p + p2 = 0 + 5 -20p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 -20p + p2 = 5 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 = 5 + 100 Reorder the terms: 100 + -20p + p2 = 5 + 100 Combine like terms: 5 + 100 = 105 100 + -20p + p2 = 105 Factor a perfect square on the left side: (p + -10)(p + -10) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (p + -10) equal to 10.246950766 and -10.246950766.Subproblem 1
p + -10 = 10.246950766 Simplifying p + -10 = 10.246950766 Reorder the terms: -10 + p = 10.246950766 Solving -10 + p = 10.246950766 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 = 10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + p = 10.246950766 + 10 p = 10.246950766 + 10 Combine like terms: 10.246950766 + 10 = 20.246950766 p = 20.246950766 Simplifying p = 20.246950766Subproblem 2
p + -10 = -10.246950766 Simplifying p + -10 = -10.246950766 Reorder the terms: -10 + p = -10.246950766 Solving -10 + p = -10.246950766 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 = -10.246950766 + 10 Combine like terms: -10 + 10 = 0 0 + p = -10.246950766 + 10 p = -10.246950766 + 10 Combine like terms: -10.246950766 + 10 = -0.246950766 p = -0.246950766 Simplifying p = -0.246950766Solution
The solution to the problem is based on the solutions from the subproblems. p = {20.246950766, -0.246950766}
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