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Simplifying p2 + 26p = 11 Reorder the terms: 26p + p2 = 11 Solving 26p + p2 = 11 Solving for variable 'p'. Reorder the terms: -11 + 26p + p2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 26p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 26p + 11 + p2 = 0 + 11 Reorder the terms: -11 + 11 + 26p + p2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 26p + p2 = 0 + 11 26p + p2 = 0 + 11 Combine like terms: 0 + 11 = 11 26p + p2 = 11 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 = 11 + 169 Reorder the terms: 169 + 26p + p2 = 11 + 169 Combine like terms: 11 + 169 = 180 169 + 26p + p2 = 180 Factor a perfect square on the left side: (p + 13)(p + 13) = 180 Calculate the square root of the right side: 13.416407865 Break this problem into two subproblems by setting (p + 13) equal to 13.416407865 and -13.416407865.Subproblem 1
p + 13 = 13.416407865 Simplifying p + 13 = 13.416407865 Reorder the terms: 13 + p = 13.416407865 Solving 13 + p = 13.416407865 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 = 13.416407865 + -13 Combine like terms: 13 + -13 = 0 0 + p = 13.416407865 + -13 p = 13.416407865 + -13 Combine like terms: 13.416407865 + -13 = 0.416407865 p = 0.416407865 Simplifying p = 0.416407865Subproblem 2
p + 13 = -13.416407865 Simplifying p + 13 = -13.416407865 Reorder the terms: 13 + p = -13.416407865 Solving 13 + p = -13.416407865 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 = -13.416407865 + -13 Combine like terms: 13 + -13 = 0 0 + p = -13.416407865 + -13 p = -13.416407865 + -13 Combine like terms: -13.416407865 + -13 = -26.416407865 p = -26.416407865 Simplifying p = -26.416407865Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.416407865, -26.416407865}
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