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Simplifying p2 + -4p = -1 Reorder the terms: -4p + p2 = -1 Solving -4p + p2 = -1 Solving for variable 'p'. Reorder the terms: 1 + -4p + p2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4p + -1 + p2 = 0 + -1 Reorder the terms: 1 + -1 + -4p + p2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4p + p2 = 0 + -1 -4p + p2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4p + p2 = -1 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = -1 + 4 Reorder the terms: 4 + -4p + p2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + -4p + p2 = 3 Factor a perfect square on the left side: (p + -2)(p + -2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (p + -2) equal to 1.732050808 and -1.732050808.Subproblem 1
p + -2 = 1.732050808 Simplifying p + -2 = 1.732050808 Reorder the terms: -2 + p = 1.732050808 Solving -2 + p = 1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + p = 1.732050808 + 2 p = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 p = 3.732050808 Simplifying p = 3.732050808Subproblem 2
p + -2 = -1.732050808 Simplifying p + -2 = -1.732050808 Reorder the terms: -2 + p = -1.732050808 Solving -2 + p = -1.732050808 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + p = -1.732050808 + 2 p = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 p = 0.267949192 Simplifying p = 0.267949192Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.732050808, 0.267949192}
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