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Simplifying 7p2 = -17p + -4 Reorder the terms: 7p2 = -4 + -17p Solving 7p2 = -4 + -17p Solving for variable 'p'. Reorder the terms: 4 + 17p + 7p2 = -4 + -17p + 4 + 17p Reorder the terms: 4 + 17p + 7p2 = -4 + 4 + -17p + 17p Combine like terms: -4 + 4 = 0 4 + 17p + 7p2 = 0 + -17p + 17p 4 + 17p + 7p2 = -17p + 17p Combine like terms: -17p + 17p = 0 4 + 17p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + 2.428571429p + p2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 2.428571429p + -0.5714285714 + p2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 2.428571429p + p2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 2.428571429p + p2 = 0 + -0.5714285714 2.428571429p + p2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 2.428571429p + p2 = -0.5714285714 The p term is 2.428571429p. Take half its coefficient (1.214285715). Square it (1.474489798) and add it to both sides. Add '1.474489798' to each side of the equation. 2.428571429p + 1.474489798 + p2 = -0.5714285714 + 1.474489798 Reorder the terms: 1.474489798 + 2.428571429p + p2 = -0.5714285714 + 1.474489798 Combine like terms: -0.5714285714 + 1.474489798 = 0.9030612266 1.474489798 + 2.428571429p + p2 = 0.9030612266 Factor a perfect square on the left side: (p + 1.214285715)(p + 1.214285715) = 0.9030612266 Calculate the square root of the right side: 0.950295337 Break this problem into two subproblems by setting (p + 1.214285715) equal to 0.950295337 and -0.950295337.Subproblem 1
p + 1.214285715 = 0.950295337 Simplifying p + 1.214285715 = 0.950295337 Reorder the terms: 1.214285715 + p = 0.950295337 Solving 1.214285715 + p = 0.950295337 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.214285715' to each side of the equation. 1.214285715 + -1.214285715 + p = 0.950295337 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + p = 0.950295337 + -1.214285715 p = 0.950295337 + -1.214285715 Combine like terms: 0.950295337 + -1.214285715 = -0.263990378 p = -0.263990378 Simplifying p = -0.263990378Subproblem 2
p + 1.214285715 = -0.950295337 Simplifying p + 1.214285715 = -0.950295337 Reorder the terms: 1.214285715 + p = -0.950295337 Solving 1.214285715 + p = -0.950295337 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.214285715' to each side of the equation. 1.214285715 + -1.214285715 + p = -0.950295337 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + p = -0.950295337 + -1.214285715 p = -0.950295337 + -1.214285715 Combine like terms: -0.950295337 + -1.214285715 = -2.164581052 p = -2.164581052 Simplifying p = -2.164581052Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.263990378, -2.164581052}
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