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Simplifying 11x2 + 33x + 12 = 0 Reorder the terms: 12 + 33x + 11x2 = 0 Solving 12 + 33x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 1.090909091 + 3x + x2 = 0 Move the constant term to the right: Add '-1.090909091' to each side of the equation. 1.090909091 + 3x + -1.090909091 + x2 = 0 + -1.090909091 Reorder the terms: 1.090909091 + -1.090909091 + 3x + x2 = 0 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + 3x + x2 = 0 + -1.090909091 3x + x2 = 0 + -1.090909091 Combine like terms: 0 + -1.090909091 = -1.090909091 3x + x2 = -1.090909091 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.090909091 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.090909091 + 2.25 Combine like terms: -1.090909091 + 2.25 = 1.159090909 2.25 + 3x + x2 = 1.159090909 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.159090909 Calculate the square root of the right side: 1.076610844 Break this problem into two subproblems by setting (x + 1.5) equal to 1.076610844 and -1.076610844.Subproblem 1
x + 1.5 = 1.076610844 Simplifying x + 1.5 = 1.076610844 Reorder the terms: 1.5 + x = 1.076610844 Solving 1.5 + x = 1.076610844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.076610844 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.076610844 + -1.5 x = 1.076610844 + -1.5 Combine like terms: 1.076610844 + -1.5 = -0.423389156 x = -0.423389156 Simplifying x = -0.423389156Subproblem 2
x + 1.5 = -1.076610844 Simplifying x + 1.5 = -1.076610844 Reorder the terms: 1.5 + x = -1.076610844 Solving 1.5 + x = -1.076610844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.076610844 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.076610844 + -1.5 x = -1.076610844 + -1.5 Combine like terms: -1.076610844 + -1.5 = -2.576610844 x = -2.576610844 Simplifying x = -2.576610844Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.423389156, -2.576610844}
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