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Simplifying 3p2 + -9 = -11p Reorder the terms: -9 + 3p2 = -11p Solving -9 + 3p2 = -11p Solving for variable 'p'. Reorder the terms: -9 + 11p + 3p2 = -11p + 11p Combine like terms: -11p + 11p = 0 -9 + 11p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 3.666666667p + p2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.666666667p + 3 + p2 = 0 + 3 Reorder the terms: -3 + 3 + 3.666666667p + p2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.666666667p + p2 = 0 + 3 3.666666667p + p2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.666666667p + p2 = 3 The p term is 3.666666667p. Take half its coefficient (1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. 3.666666667p + 3.361111114 + p2 = 3 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667p + p2 = 3 + 3.361111114 Combine like terms: 3 + 3.361111114 = 6.361111114 3.361111114 + 3.666666667p + p2 = 6.361111114 Factor a perfect square on the left side: (p + 1.833333334)(p + 1.833333334) = 6.361111114 Calculate the square root of the right side: 2.522124326 Break this problem into two subproblems by setting (p + 1.833333334) equal to 2.522124326 and -2.522124326.Subproblem 1
p + 1.833333334 = 2.522124326 Simplifying p + 1.833333334 = 2.522124326 Reorder the terms: 1.833333334 + p = 2.522124326 Solving 1.833333334 + p = 2.522124326 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + p = 2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + p = 2.522124326 + -1.833333334 p = 2.522124326 + -1.833333334 Combine like terms: 2.522124326 + -1.833333334 = 0.688790992 p = 0.688790992 Simplifying p = 0.688790992Subproblem 2
p + 1.833333334 = -2.522124326 Simplifying p + 1.833333334 = -2.522124326 Reorder the terms: 1.833333334 + p = -2.522124326 Solving 1.833333334 + p = -2.522124326 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + p = -2.522124326 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + p = -2.522124326 + -1.833333334 p = -2.522124326 + -1.833333334 Combine like terms: -2.522124326 + -1.833333334 = -4.35545766 p = -4.35545766 Simplifying p = -4.35545766Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.688790992, -4.35545766}
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