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Simplifying 63p + -16p2 = 17 Solving 63p + -16p2 = 17 Solving for variable 'p'. Reorder the terms: -17 + 63p + -16p2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 63p + -16p2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.0625 + -3.9375p + p2 = 0 Move the constant term to the right: Add '-1.0625' to each side of the equation. 1.0625 + -3.9375p + -1.0625 + p2 = 0 + -1.0625 Reorder the terms: 1.0625 + -1.0625 + -3.9375p + p2 = 0 + -1.0625 Combine like terms: 1.0625 + -1.0625 = 0.0000 0.0000 + -3.9375p + p2 = 0 + -1.0625 -3.9375p + p2 = 0 + -1.0625 Combine like terms: 0 + -1.0625 = -1.0625 -3.9375p + p2 = -1.0625 The p term is -3.9375p. Take half its coefficient (-1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. -3.9375p + 3.875976563 + p2 = -1.0625 + 3.875976563 Reorder the terms: 3.875976563 + -3.9375p + p2 = -1.0625 + 3.875976563 Combine like terms: -1.0625 + 3.875976563 = 2.813476563 3.875976563 + -3.9375p + p2 = 2.813476563 Factor a perfect square on the left side: (p + -1.96875)(p + -1.96875) = 2.813476563 Calculate the square root of the right side: 1.677342113 Break this problem into two subproblems by setting (p + -1.96875) equal to 1.677342113 and -1.677342113.Subproblem 1
p + -1.96875 = 1.677342113 Simplifying p + -1.96875 = 1.677342113 Reorder the terms: -1.96875 + p = 1.677342113 Solving -1.96875 + p = 1.677342113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + p = 1.677342113 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + p = 1.677342113 + 1.96875 p = 1.677342113 + 1.96875 Combine like terms: 1.677342113 + 1.96875 = 3.646092113 p = 3.646092113 Simplifying p = 3.646092113Subproblem 2
p + -1.96875 = -1.677342113 Simplifying p + -1.96875 = -1.677342113 Reorder the terms: -1.96875 + p = -1.677342113 Solving -1.96875 + p = -1.677342113 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.96875' to each side of the equation. -1.96875 + 1.96875 + p = -1.677342113 + 1.96875 Combine like terms: -1.96875 + 1.96875 = 0.00000 0.00000 + p = -1.677342113 + 1.96875 p = -1.677342113 + 1.96875 Combine like terms: -1.677342113 + 1.96875 = 0.291407887 p = 0.291407887 Simplifying p = 0.291407887Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.646092113, 0.291407887}
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