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Simplifying 7p2 + 3p + -7 = 0 Reorder the terms: -7 + 3p + 7p2 = 0 Solving -7 + 3p + 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 + 0.4285714286p + p2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4285714286p + 1 + p2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4285714286p + p2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4285714286p + p2 = 0 + 1 0.4285714286p + p2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4285714286p + p2 = 1 The p term is 0.4285714286p. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286p + 0.04591836735 + p2 = 1 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286p + p2 = 1 + 0.04591836735 Combine like terms: 1 + 0.04591836735 = 1.04591836735 0.04591836735 + 0.4285714286p + p2 = 1.04591836735 Factor a perfect square on the left side: (p + 0.2142857143)(p + 0.2142857143) = 1.04591836735 Calculate the square root of the right side: 1.022701505 Break this problem into two subproblems by setting (p + 0.2142857143) equal to 1.022701505 and -1.022701505.Subproblem 1
p + 0.2142857143 = 1.022701505 Simplifying p + 0.2142857143 = 1.022701505 Reorder the terms: 0.2142857143 + p = 1.022701505 Solving 0.2142857143 + p = 1.022701505 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + p = 1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + p = 1.022701505 + -0.2142857143 p = 1.022701505 + -0.2142857143 Combine like terms: 1.022701505 + -0.2142857143 = 0.8084157907 p = 0.8084157907 Simplifying p = 0.8084157907Subproblem 2
p + 0.2142857143 = -1.022701505 Simplifying p + 0.2142857143 = -1.022701505 Reorder the terms: 0.2142857143 + p = -1.022701505 Solving 0.2142857143 + p = -1.022701505 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + p = -1.022701505 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + p = -1.022701505 + -0.2142857143 p = -1.022701505 + -0.2142857143 Combine like terms: -1.022701505 + -0.2142857143 = -1.2369872193 p = -1.2369872193 Simplifying p = -1.2369872193Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.8084157907, -1.2369872193}
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