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Simplifying 7p2 + -22 = -11p Reorder the terms: -22 + 7p2 = -11p Solving -22 + 7p2 = -11p Solving for variable 'p'. Reorder the terms: -22 + 11p + 7p2 = -11p + 11p Combine like terms: -11p + 11p = 0 -22 + 11p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.142857143 + 1.571428571p + p2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + 1.571428571p + 3.142857143 + p2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + 1.571428571p + p2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + 1.571428571p + p2 = 0 + 3.142857143 1.571428571p + p2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 1.571428571p + p2 = 3.142857143 The p term is 1.571428571p. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571p + 0.6173469384 + p2 = 3.142857143 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571p + p2 = 3.142857143 + 0.6173469384 Combine like terms: 3.142857143 + 0.6173469384 = 3.7602040814 0.6173469384 + 1.571428571p + p2 = 3.7602040814 Factor a perfect square on the left side: (p + 0.7857142855)(p + 0.7857142855) = 3.7602040814 Calculate the square root of the right side: 1.939124566 Break this problem into two subproblems by setting (p + 0.7857142855) equal to 1.939124566 and -1.939124566.Subproblem 1
p + 0.7857142855 = 1.939124566 Simplifying p + 0.7857142855 = 1.939124566 Reorder the terms: 0.7857142855 + p = 1.939124566 Solving 0.7857142855 + p = 1.939124566 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + p = 1.939124566 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + p = 1.939124566 + -0.7857142855 p = 1.939124566 + -0.7857142855 Combine like terms: 1.939124566 + -0.7857142855 = 1.1534102805 p = 1.1534102805 Simplifying p = 1.1534102805Subproblem 2
p + 0.7857142855 = -1.939124566 Simplifying p + 0.7857142855 = -1.939124566 Reorder the terms: 0.7857142855 + p = -1.939124566 Solving 0.7857142855 + p = -1.939124566 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + p = -1.939124566 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + p = -1.939124566 + -0.7857142855 p = -1.939124566 + -0.7857142855 Combine like terms: -1.939124566 + -0.7857142855 = -2.7248388515 p = -2.7248388515 Simplifying p = -2.7248388515Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.1534102805, -2.7248388515}
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