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Simplifying 6p2 + 9p + -46 = 0 Reorder the terms: -46 + 9p + 6p2 = 0 Solving -46 + 9p + 6p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.666666667 + 1.5p + p2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 1.5p + 7.666666667 + p2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 1.5p + p2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 1.5p + p2 = 0 + 7.666666667 1.5p + p2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 1.5p + p2 = 7.666666667 The p term is 1.5p. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5p + 0.5625 + p2 = 7.666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5p + p2 = 7.666666667 + 0.5625 Combine like terms: 7.666666667 + 0.5625 = 8.229166667 0.5625 + 1.5p + p2 = 8.229166667 Factor a perfect square on the left side: (p + 0.75)(p + 0.75) = 8.229166667 Calculate the square root of the right side: 2.868652413 Break this problem into two subproblems by setting (p + 0.75) equal to 2.868652413 and -2.868652413.Subproblem 1
p + 0.75 = 2.868652413 Simplifying p + 0.75 = 2.868652413 Reorder the terms: 0.75 + p = 2.868652413 Solving 0.75 + p = 2.868652413 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = 2.868652413 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = 2.868652413 + -0.75 p = 2.868652413 + -0.75 Combine like terms: 2.868652413 + -0.75 = 2.118652413 p = 2.118652413 Simplifying p = 2.118652413Subproblem 2
p + 0.75 = -2.868652413 Simplifying p + 0.75 = -2.868652413 Reorder the terms: 0.75 + p = -2.868652413 Solving 0.75 + p = -2.868652413 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + p = -2.868652413 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + p = -2.868652413 + -0.75 p = -2.868652413 + -0.75 Combine like terms: -2.868652413 + -0.75 = -3.618652413 p = -3.618652413 Simplifying p = -3.618652413Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.118652413, -3.618652413}
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