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Simplifying p2 + -22p = -45 Reorder the terms: -22p + p2 = -45 Solving -22p + p2 = -45 Solving for variable 'p'. Reorder the terms: 45 + -22p + p2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + -22p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -22p + -45 + p2 = 0 + -45 Reorder the terms: 45 + -45 + -22p + p2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -22p + p2 = 0 + -45 -22p + p2 = 0 + -45 Combine like terms: 0 + -45 = -45 -22p + p2 = -45 The p term is -22p. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22p + 121 + p2 = -45 + 121 Reorder the terms: 121 + -22p + p2 = -45 + 121 Combine like terms: -45 + 121 = 76 121 + -22p + p2 = 76 Factor a perfect square on the left side: (p + -11)(p + -11) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (p + -11) equal to 8.717797887 and -8.717797887.Subproblem 1
p + -11 = 8.717797887 Simplifying p + -11 = 8.717797887 Reorder the terms: -11 + p = 8.717797887 Solving -11 + p = 8.717797887 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + p = 8.717797887 + 11 Combine like terms: -11 + 11 = 0 0 + p = 8.717797887 + 11 p = 8.717797887 + 11 Combine like terms: 8.717797887 + 11 = 19.717797887 p = 19.717797887 Simplifying p = 19.717797887Subproblem 2
p + -11 = -8.717797887 Simplifying p + -11 = -8.717797887 Reorder the terms: -11 + p = -8.717797887 Solving -11 + p = -8.717797887 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + p = -8.717797887 + 11 Combine like terms: -11 + 11 = 0 0 + p = -8.717797887 + 11 p = -8.717797887 + 11 Combine like terms: -8.717797887 + 11 = 2.282202113 p = 2.282202113 Simplifying p = 2.282202113Solution
The solution to the problem is based on the solutions from the subproblems. p = {19.717797887, 2.282202113}
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