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Simplifying 6p2 + 5p + -12 = 0 Reorder the terms: -12 + 5p + 6p2 = 0 Solving -12 + 5p + 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'. -2 + 0.8333333333p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.8333333333p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + 0.8333333333p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.8333333333p + p2 = 0 + 2 0.8333333333p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.8333333333p + p2 = 2 The p term is 0.8333333333p. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333p + 0.1736111111 + p2 = 2 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333p + p2 = 2 + 0.1736111111 Combine like terms: 2 + 0.1736111111 = 2.1736111111 0.1736111111 + 0.8333333333p + p2 = 2.1736111111 Factor a perfect square on the left side: (p + 0.4166666667)(p + 0.4166666667) = 2.1736111111 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (p + 0.4166666667) equal to 1.474317168 and -1.474317168.Subproblem 1
p + 0.4166666667 = 1.474317168 Simplifying p + 0.4166666667 = 1.474317168 Reorder the terms: 0.4166666667 + p = 1.474317168 Solving 0.4166666667 + p = 1.474317168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + p = 1.474317168 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + p = 1.474317168 + -0.4166666667 p = 1.474317168 + -0.4166666667 Combine like terms: 1.474317168 + -0.4166666667 = 1.0576505013 p = 1.0576505013 Simplifying p = 1.0576505013Subproblem 2
p + 0.4166666667 = -1.474317168 Simplifying p + 0.4166666667 = -1.474317168 Reorder the terms: 0.4166666667 + p = -1.474317168 Solving 0.4166666667 + p = -1.474317168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + p = -1.474317168 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + p = -1.474317168 + -0.4166666667 p = -1.474317168 + -0.4166666667 Combine like terms: -1.474317168 + -0.4166666667 = -1.8909838347 p = -1.8909838347 Simplifying p = -1.8909838347Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.0576505013, -1.8909838347}
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