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Simplifying 12x2 + -11x = 55 Reorder the terms: -11x + 12x2 = 55 Solving -11x + 12x2 = 55 Solving for variable 'x'. Reorder the terms: -55 + -11x + 12x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + -11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -4.583333333 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '4.583333333' to each side of the equation. -4.583333333 + -0.9166666667x + 4.583333333 + x2 = 0 + 4.583333333 Reorder the terms: -4.583333333 + 4.583333333 + -0.9166666667x + x2 = 0 + 4.583333333 Combine like terms: -4.583333333 + 4.583333333 = 0.000000000 0.000000000 + -0.9166666667x + x2 = 0 + 4.583333333 -0.9166666667x + x2 = 0 + 4.583333333 Combine like terms: 0 + 4.583333333 = 4.583333333 -0.9166666667x + x2 = 4.583333333 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 = 4.583333333 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 4.583333333 + 0.2100694445 Combine like terms: 4.583333333 + 0.2100694445 = 4.7934027775 0.2100694445 + -0.9166666667x + x2 = 4.7934027775 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 4.7934027775 Calculate the square root of the right side: 2.189384109 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 2.189384109 and -2.189384109.Subproblem 1
x + -0.4583333334 = 2.189384109 Simplifying x + -0.4583333334 = 2.189384109 Reorder the terms: -0.4583333334 + x = 2.189384109 Solving -0.4583333334 + x = 2.189384109 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 = 2.189384109 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 2.189384109 + 0.4583333334 x = 2.189384109 + 0.4583333334 Combine like terms: 2.189384109 + 0.4583333334 = 2.6477174424 x = 2.6477174424 Simplifying x = 2.6477174424Subproblem 2
x + -0.4583333334 = -2.189384109 Simplifying x + -0.4583333334 = -2.189384109 Reorder the terms: -0.4583333334 + x = -2.189384109 Solving -0.4583333334 + x = -2.189384109 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 = -2.189384109 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -2.189384109 + 0.4583333334 x = -2.189384109 + 0.4583333334 Combine like terms: -2.189384109 + 0.4583333334 = -1.7310507756 x = -1.7310507756 Simplifying x = -1.7310507756Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6477174424, -1.7310507756}
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