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Simplifying 7p2 + -9p + -7 = 0 Reorder the terms: -7 + -9p + 7p2 = 0 Solving -7 + -9p + 7p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + -1.285714286p + p2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.285714286p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + -1.285714286p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.285714286p + p2 = 0 + 1 -1.285714286p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.285714286p + p2 = 1 The p term is -1.285714286p. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286p + 0.4132653063 + p2 = 1 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286p + p2 = 1 + 0.4132653063 Combine like terms: 1 + 0.4132653063 = 1.4132653063 0.4132653063 + -1.285714286p + p2 = 1.4132653063 Factor a perfect square on the left side: (p + -0.642857143)(p + -0.642857143) = 1.4132653063 Calculate the square root of the right side: 1.188808356 Break this problem into two subproblems by setting (p + -0.642857143) equal to 1.188808356 and -1.188808356.Subproblem 1
p + -0.642857143 = 1.188808356 Simplifying p + -0.642857143 = 1.188808356 Reorder the terms: -0.642857143 + p = 1.188808356 Solving -0.642857143 + p = 1.188808356 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + p = 1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + p = 1.188808356 + 0.642857143 p = 1.188808356 + 0.642857143 Combine like terms: 1.188808356 + 0.642857143 = 1.831665499 p = 1.831665499 Simplifying p = 1.831665499Subproblem 2
p + -0.642857143 = -1.188808356 Simplifying p + -0.642857143 = -1.188808356 Reorder the terms: -0.642857143 + p = -1.188808356 Solving -0.642857143 + p = -1.188808356 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + p = -1.188808356 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + p = -1.188808356 + 0.642857143 p = -1.188808356 + 0.642857143 Combine like terms: -1.188808356 + 0.642857143 = -0.545951213 p = -0.545951213 Simplifying p = -0.545951213Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.831665499, -0.545951213}
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