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Simplifying p2 + -6p = -4 Reorder the terms: -6p + p2 = -4 Solving -6p + p2 = -4 Solving for variable 'p'. Reorder the terms: 4 + -6p + p2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6p + -4 + p2 = 0 + -4 Reorder the terms: 4 + -4 + -6p + p2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6p + p2 = 0 + -4 -6p + p2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6p + p2 = -4 The p term is -6p. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6p + 9 + p2 = -4 + 9 Reorder the terms: 9 + -6p + p2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6p + p2 = 5 Factor a perfect square on the left side: (p + -3)(p + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (p + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
p + -3 = 2.236067978 Simplifying p + -3 = 2.236067978 Reorder the terms: -3 + p = 2.236067978 Solving -3 + p = 2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + p = 2.236067978 + 3 p = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 p = 5.236067978 Simplifying p = 5.236067978Subproblem 2
p + -3 = -2.236067978 Simplifying p + -3 = -2.236067978 Reorder the terms: -3 + p = -2.236067978 Solving -3 + p = -2.236067978 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + p = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + p = -2.236067978 + 3 p = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 p = 0.763932022 Simplifying p = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. p = {5.236067978, 0.763932022}
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