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Simplifying 9x2 + 33x + 11 = 0 Reorder the terms: 11 + 33x + 9x2 = 0 Solving 11 + 33x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.222222222 + 3.666666667x + x2 = 0 Move the constant term to the right: Add '-1.222222222' to each side of the equation. 1.222222222 + 3.666666667x + -1.222222222 + x2 = 0 + -1.222222222 Reorder the terms: 1.222222222 + -1.222222222 + 3.666666667x + x2 = 0 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + 3.666666667x + x2 = 0 + -1.222222222 3.666666667x + x2 = 0 + -1.222222222 Combine like terms: 0 + -1.222222222 = -1.222222222 3.666666667x + x2 = -1.222222222 The x term is 3.666666667x. 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. 3.666666667x + 3.361111114 + x2 = -1.222222222 + 3.361111114 Reorder the terms: 3.361111114 + 3.666666667x + x2 = -1.222222222 + 3.361111114 Combine like terms: -1.222222222 + 3.361111114 = 2.138888892 3.361111114 + 3.666666667x + x2 = 2.138888892 Factor a perfect square on the left side: (x + 1.833333334)(x + 1.833333334) = 2.138888892 Calculate the square root of the right side: 1.462494066 Break this problem into two subproblems by setting (x + 1.833333334) equal to 1.462494066 and -1.462494066.Subproblem 1
x + 1.833333334 = 1.462494066 Simplifying x + 1.833333334 = 1.462494066 Reorder the terms: 1.833333334 + x = 1.462494066 Solving 1.833333334 + x = 1.462494066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = 1.462494066 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = 1.462494066 + -1.833333334 x = 1.462494066 + -1.833333334 Combine like terms: 1.462494066 + -1.833333334 = -0.370839268 x = -0.370839268 Simplifying x = -0.370839268Subproblem 2
x + 1.833333334 = -1.462494066 Simplifying x + 1.833333334 = -1.462494066 Reorder the terms: 1.833333334 + x = -1.462494066 Solving 1.833333334 + x = -1.462494066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + x = -1.462494066 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + x = -1.462494066 + -1.833333334 x = -1.462494066 + -1.833333334 Combine like terms: -1.462494066 + -1.833333334 = -3.2958274 x = -3.2958274 Simplifying x = -3.2958274Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.370839268, -3.2958274}
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