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Simplifying 3a2 + 11a + -33 = 0 Reorder the terms: -33 + 11a + 3a2 = 0 Solving -33 + 11a + 3a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + 3.666666667a + a2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 3.666666667a + 11 + a2 = 0 + 11 Reorder the terms: -11 + 11 + 3.666666667a + a2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 3.666666667a + a2 = 0 + 11 3.666666667a + a2 = 0 + 11 Combine like terms: 0 + 11 = 11 3.666666667a + a2 = 11 The a term is 3.666666667a. 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. 3.666666667a + 3.361111114 + a2 = 11 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667a + a2 = 11 + 3.361111114 Combine like terms: 11 + 3.361111114 = 14.361111114 3.361111114 + 3.666666667a + a2 = 14.361111114 Factor a perfect square on the left side: (a + 1.833333334)(a + 1.833333334) = 14.361111114 Calculate the square root of the right side: 3.789605667 Break this problem into two subproblems by setting (a + 1.833333334) equal to 3.789605667 and -3.789605667.Subproblem 1
a + 1.833333334 = 3.789605667 Simplifying a + 1.833333334 = 3.789605667 Reorder the terms: 1.833333334 + a = 3.789605667 Solving 1.833333334 + a = 3.789605667 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + a = 3.789605667 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + a = 3.789605667 + -1.833333334 a = 3.789605667 + -1.833333334 Combine like terms: 3.789605667 + -1.833333334 = 1.956272333 a = 1.956272333 Simplifying a = 1.956272333Subproblem 2
a + 1.833333334 = -3.789605667 Simplifying a + 1.833333334 = -3.789605667 Reorder the terms: 1.833333334 + a = -3.789605667 Solving 1.833333334 + a = -3.789605667 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + a = -3.789605667 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + a = -3.789605667 + -1.833333334 a = -3.789605667 + -1.833333334 Combine like terms: -3.789605667 + -1.833333334 = -5.622939001 a = -5.622939001 Simplifying a = -5.622939001Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.956272333, -5.622939001}
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