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Simplifying 49p2 + -112p + -64 = 0 Reorder the terms: -64 + -112p + 49p2 = 0 Solving -64 + -112p + 49p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -1.306122449 + -2.285714286p + p2 = 0 Move the constant term to the right: Add '1.306122449' to each side of the equation. -1.306122449 + -2.285714286p + 1.306122449 + p2 = 0 + 1.306122449 Reorder the terms: -1.306122449 + 1.306122449 + -2.285714286p + p2 = 0 + 1.306122449 Combine like terms: -1.306122449 + 1.306122449 = 0.000000000 0.000000000 + -2.285714286p + p2 = 0 + 1.306122449 -2.285714286p + p2 = 0 + 1.306122449 Combine like terms: 0 + 1.306122449 = 1.306122449 -2.285714286p + p2 = 1.306122449 The p term is -2.285714286p. Take half its coefficient (-1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. -2.285714286p + 1.306122449 + p2 = 1.306122449 + 1.306122449 Reorder the terms: 1.306122449 + -2.285714286p + p2 = 1.306122449 + 1.306122449 Combine like terms: 1.306122449 + 1.306122449 = 2.612244898 1.306122449 + -2.285714286p + p2 = 2.612244898 Factor a perfect square on the left side: (p + -1.142857143)(p + -1.142857143) = 2.612244898 Calculate the square root of the right side: 1.616244071 Break this problem into two subproblems by setting (p + -1.142857143) equal to 1.616244071 and -1.616244071.Subproblem 1
p + -1.142857143 = 1.616244071 Simplifying p + -1.142857143 = 1.616244071 Reorder the terms: -1.142857143 + p = 1.616244071 Solving -1.142857143 + p = 1.616244071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + p = 1.616244071 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + p = 1.616244071 + 1.142857143 p = 1.616244071 + 1.142857143 Combine like terms: 1.616244071 + 1.142857143 = 2.759101214 p = 2.759101214 Simplifying p = 2.759101214Subproblem 2
p + -1.142857143 = -1.616244071 Simplifying p + -1.142857143 = -1.616244071 Reorder the terms: -1.142857143 + p = -1.616244071 Solving -1.142857143 + p = -1.616244071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + p = -1.616244071 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + p = -1.616244071 + 1.142857143 p = -1.616244071 + 1.142857143 Combine like terms: -1.616244071 + 1.142857143 = -0.473386928 p = -0.473386928 Simplifying p = -0.473386928Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.759101214, -0.473386928}
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