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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 = 5 4 + -4p + p2 = 5 Factor a perfect square on the left side: (p + -2)(p + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (p + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
p + -2 = 2.236067978 Simplifying p + -2 = 2.236067978 Reorder the terms: -2 + p = 2.236067978 Solving -2 + p = 2.236067978 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 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + p = 2.236067978 + 2 p = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 p = 4.236067978 Simplifying p = 4.236067978Subproblem 2
p + -2 = -2.236067978 Simplifying p + -2 = -2.236067978 Reorder the terms: -2 + p = -2.236067978 Solving -2 + p = -2.236067978 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 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + p = -2.236067978 + 2 p = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 p = -0.236067978 Simplifying p = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.236067978, -0.236067978}
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