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Simplifying 12p2 + 1 = -9p Reorder the terms: 1 + 12p2 = -9p Solving 1 + 12p2 = -9p Solving for variable 'p'. Reorder the terms: 1 + 9p + 12p2 = -9p + 9p Combine like terms: -9p + 9p = 0 1 + 9p + 12p2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + 0.75p + p2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 0.75p + -0.08333333333 + p2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 0.75p + p2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 0.75p + p2 = 0 + -0.08333333333 0.75p + p2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 0.75p + p2 = -0.08333333333 The p term is 0.75p. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75p + 0.140625 + p2 = -0.08333333333 + 0.140625 Reorder the terms: 0.140625 + 0.75p + p2 = -0.08333333333 + 0.140625 Combine like terms: -0.08333333333 + 0.140625 = 0.05729166667 0.140625 + 0.75p + p2 = 0.05729166667 Factor a perfect square on the left side: (p + 0.375)(p + 0.375) = 0.05729166667 Calculate the square root of the right side: 0.239356777 Break this problem into two subproblems by setting (p + 0.375) equal to 0.239356777 and -0.239356777.Subproblem 1
p + 0.375 = 0.239356777 Simplifying p + 0.375 = 0.239356777 Reorder the terms: 0.375 + p = 0.239356777 Solving 0.375 + p = 0.239356777 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = 0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = 0.239356777 + -0.375 p = 0.239356777 + -0.375 Combine like terms: 0.239356777 + -0.375 = -0.135643223 p = -0.135643223 Simplifying p = -0.135643223Subproblem 2
p + 0.375 = -0.239356777 Simplifying p + 0.375 = -0.239356777 Reorder the terms: 0.375 + p = -0.239356777 Solving 0.375 + p = -0.239356777 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + p = -0.239356777 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + p = -0.239356777 + -0.375 p = -0.239356777 + -0.375 Combine like terms: -0.239356777 + -0.375 = -0.614356777 p = -0.614356777 Simplifying p = -0.614356777Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.135643223, -0.614356777}
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