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Simplifying p2 + -26p = 41 Reorder the terms: -26p + p2 = 41 Solving -26p + p2 = 41 Solving for variable 'p'. Reorder the terms: -41 + -26p + p2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -26p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -26p + 41 + p2 = 0 + 41 Reorder the terms: -41 + 41 + -26p + p2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -26p + p2 = 0 + 41 -26p + p2 = 0 + 41 Combine like terms: 0 + 41 = 41 -26p + p2 = 41 The p term is -26p. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26p + 169 + p2 = 41 + 169 Reorder the terms: 169 + -26p + p2 = 41 + 169 Combine like terms: 41 + 169 = 210 169 + -26p + p2 = 210 Factor a perfect square on the left side: (p + -13)(p + -13) = 210 Calculate the square root of the right side: 14.491376746 Break this problem into two subproblems by setting (p + -13) equal to 14.491376746 and -14.491376746.Subproblem 1
p + -13 = 14.491376746 Simplifying p + -13 = 14.491376746 Reorder the terms: -13 + p = 14.491376746 Solving -13 + p = 14.491376746 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + p = 14.491376746 + 13 Combine like terms: -13 + 13 = 0 0 + p = 14.491376746 + 13 p = 14.491376746 + 13 Combine like terms: 14.491376746 + 13 = 27.491376746 p = 27.491376746 Simplifying p = 27.491376746Subproblem 2
p + -13 = -14.491376746 Simplifying p + -13 = -14.491376746 Reorder the terms: -13 + p = -14.491376746 Solving -13 + p = -14.491376746 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + p = -14.491376746 + 13 Combine like terms: -13 + 13 = 0 0 + p = -14.491376746 + 13 p = -14.491376746 + 13 Combine like terms: -14.491376746 + 13 = -1.491376746 p = -1.491376746 Simplifying p = -1.491376746Solution
The solution to the problem is based on the solutions from the subproblems. p = {27.491376746, -1.491376746}
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