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Simplifying 7p2 + -22 = -8p Reorder the terms: -22 + 7p2 = -8p Solving -22 + 7p2 = -8p Solving for variable 'p'. Reorder the terms: -22 + 8p + 7p2 = -8p + 8p Combine like terms: -8p + 8p = 0 -22 + 8p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.142857143 + 1.142857143p + p2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + 1.142857143p + 3.142857143 + p2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + 1.142857143p + p2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + 1.142857143p + p2 = 0 + 3.142857143 1.142857143p + p2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 1.142857143p + p2 = 3.142857143 The p term is 1.142857143p. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143p + 0.3265306123 + p2 = 3.142857143 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143p + p2 = 3.142857143 + 0.3265306123 Combine like terms: 3.142857143 + 0.3265306123 = 3.4693877553 0.3265306123 + 1.142857143p + p2 = 3.4693877553 Factor a perfect square on the left side: (p + 0.5714285715)(p + 0.5714285715) = 3.4693877553 Calculate the square root of the right side: 1.862629259 Break this problem into two subproblems by setting (p + 0.5714285715) equal to 1.862629259 and -1.862629259.Subproblem 1
p + 0.5714285715 = 1.862629259 Simplifying p + 0.5714285715 = 1.862629259 Reorder the terms: 0.5714285715 + p = 1.862629259 Solving 0.5714285715 + p = 1.862629259 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + p = 1.862629259 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + p = 1.862629259 + -0.5714285715 p = 1.862629259 + -0.5714285715 Combine like terms: 1.862629259 + -0.5714285715 = 1.2912006875 p = 1.2912006875 Simplifying p = 1.2912006875Subproblem 2
p + 0.5714285715 = -1.862629259 Simplifying p + 0.5714285715 = -1.862629259 Reorder the terms: 0.5714285715 + p = -1.862629259 Solving 0.5714285715 + p = -1.862629259 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5714285715' to each side of the equation. 0.5714285715 + -0.5714285715 + p = -1.862629259 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + p = -1.862629259 + -0.5714285715 p = -1.862629259 + -0.5714285715 Combine like terms: -1.862629259 + -0.5714285715 = -2.4340578305 p = -2.4340578305 Simplifying p = -2.4340578305Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.2912006875, -2.4340578305}
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