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Simplifying 7p2 = -6p + 3 Reorder the terms: 7p2 = 3 + -6p Solving 7p2 = 3 + -6p Solving for variable 'p'. Reorder the terms: -3 + 6p + 7p2 = 3 + -6p + -3 + 6p Reorder the terms: -3 + 6p + 7p2 = 3 + -3 + -6p + 6p Combine like terms: 3 + -3 = 0 -3 + 6p + 7p2 = 0 + -6p + 6p -3 + 6p + 7p2 = -6p + 6p Combine like terms: -6p + 6p = 0 -3 + 6p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + 0.8571428571p + p2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.8571428571p + 0.4285714286 + p2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.8571428571p + p2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.8571428571p + p2 = 0 + 0.4285714286 0.8571428571p + p2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.8571428571p + p2 = 0.4285714286 The p term is 0.8571428571p. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571p + 0.1836734694 + p2 = 0.4285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571p + p2 = 0.4285714286 + 0.1836734694 Combine like terms: 0.4285714286 + 0.1836734694 = 0.612244898 0.1836734694 + 0.8571428571p + p2 = 0.612244898 Factor a perfect square on the left side: (p + 0.4285714286)(p + 0.4285714286) = 0.612244898 Calculate the square root of the right side: 0.782460796 Break this problem into two subproblems by setting (p + 0.4285714286) equal to 0.782460796 and -0.782460796.Subproblem 1
p + 0.4285714286 = 0.782460796 Simplifying p + 0.4285714286 = 0.782460796 Reorder the terms: 0.4285714286 + p = 0.782460796 Solving 0.4285714286 + p = 0.782460796 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + p = 0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + p = 0.782460796 + -0.4285714286 p = 0.782460796 + -0.4285714286 Combine like terms: 0.782460796 + -0.4285714286 = 0.3538893674 p = 0.3538893674 Simplifying p = 0.3538893674Subproblem 2
p + 0.4285714286 = -0.782460796 Simplifying p + 0.4285714286 = -0.782460796 Reorder the terms: 0.4285714286 + p = -0.782460796 Solving 0.4285714286 + p = -0.782460796 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + p = -0.782460796 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + p = -0.782460796 + -0.4285714286 p = -0.782460796 + -0.4285714286 Combine like terms: -0.782460796 + -0.4285714286 = -1.2110322246 p = -1.2110322246 Simplifying p = -1.2110322246Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.3538893674, -1.2110322246}
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