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Simplifying 6p2 = 9 + -7p Solving 6p2 = 9 + -7p Solving for variable 'p'. Reorder the terms: -9 + 7p + 6p2 = 9 + -7p + -9 + 7p Reorder the terms: -9 + 7p + 6p2 = 9 + -9 + -7p + 7p Combine like terms: 9 + -9 = 0 -9 + 7p + 6p2 = 0 + -7p + 7p -9 + 7p + 6p2 = -7p + 7p Combine like terms: -7p + 7p = 0 -9 + 7p + 6p2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 1.166666667p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.166666667p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.166666667p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.166666667p + p2 = 0 + 1.5 1.166666667p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.166666667p + p2 = 1.5 The p term is 1.166666667p. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667p + 0.3402777780 + p2 = 1.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667p + p2 = 1.5 + 0.3402777780 Combine like terms: 1.5 + 0.3402777780 = 1.840277778 0.3402777780 + 1.166666667p + p2 = 1.840277778 Factor a perfect square on the left side: (p + 0.5833333335)(p + 0.5833333335) = 1.840277778 Calculate the square root of the right side: 1.356568383 Break this problem into two subproblems by setting (p + 0.5833333335) equal to 1.356568383 and -1.356568383.Subproblem 1
p + 0.5833333335 = 1.356568383 Simplifying p + 0.5833333335 = 1.356568383 Reorder the terms: 0.5833333335 + p = 1.356568383 Solving 0.5833333335 + p = 1.356568383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + p = 1.356568383 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + p = 1.356568383 + -0.5833333335 p = 1.356568383 + -0.5833333335 Combine like terms: 1.356568383 + -0.5833333335 = 0.7732350495 p = 0.7732350495 Simplifying p = 0.7732350495Subproblem 2
p + 0.5833333335 = -1.356568383 Simplifying p + 0.5833333335 = -1.356568383 Reorder the terms: 0.5833333335 + p = -1.356568383 Solving 0.5833333335 + p = -1.356568383 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + p = -1.356568383 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + p = -1.356568383 + -0.5833333335 p = -1.356568383 + -0.5833333335 Combine like terms: -1.356568383 + -0.5833333335 = -1.9399017165 p = -1.9399017165 Simplifying p = -1.9399017165Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.7732350495, -1.9399017165}
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