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Simplifying 12x2 + 11x + -72 = 0 Reorder the terms: -72 + 11x + 12x2 = 0 Solving -72 + 11x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -6 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.9166666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.9166666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.9166666667x + x2 = 0 + 6 0.9166666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.9166666667x + x2 = 6 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 6 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 6 + 0.2100694445 Combine like terms: 6 + 0.2100694445 = 6.2100694445 0.2100694445 + 0.9166666667x + x2 = 6.2100694445 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 6.2100694445 Calculate the square root of the right side: 2.492001092 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 2.492001092 and -2.492001092.Subproblem 1
x + 0.4583333334 = 2.492001092 Simplifying x + 0.4583333334 = 2.492001092 Reorder the terms: 0.4583333334 + x = 2.492001092 Solving 0.4583333334 + x = 2.492001092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 2.492001092 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 2.492001092 + -0.4583333334 x = 2.492001092 + -0.4583333334 Combine like terms: 2.492001092 + -0.4583333334 = 2.0336677586 x = 2.0336677586 Simplifying x = 2.0336677586Subproblem 2
x + 0.4583333334 = -2.492001092 Simplifying x + 0.4583333334 = -2.492001092 Reorder the terms: 0.4583333334 + x = -2.492001092 Solving 0.4583333334 + x = -2.492001092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -2.492001092 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -2.492001092 + -0.4583333334 x = -2.492001092 + -0.4583333334 Combine like terms: -2.492001092 + -0.4583333334 = -2.9503344254 x = -2.9503344254 Simplifying x = -2.9503344254Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0336677586, -2.9503344254}
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