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Simplifying 11x2 + -76x + -184 = 0 Reorder the terms: -184 + -76x + 11x2 = 0 Solving -184 + -76x + 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'. -16.72727273 + -6.909090909x + x2 = 0 Move the constant term to the right: Add '16.72727273' to each side of the equation. -16.72727273 + -6.909090909x + 16.72727273 + x2 = 0 + 16.72727273 Reorder the terms: -16.72727273 + 16.72727273 + -6.909090909x + x2 = 0 + 16.72727273 Combine like terms: -16.72727273 + 16.72727273 = 0.00000000 0.00000000 + -6.909090909x + x2 = 0 + 16.72727273 -6.909090909x + x2 = 0 + 16.72727273 Combine like terms: 0 + 16.72727273 = 16.72727273 -6.909090909x + x2 = 16.72727273 The x term is -6.909090909x. Take half its coefficient (-3.454545455). Square it (11.93388430) and add it to both sides. Add '11.93388430' to each side of the equation. -6.909090909x + 11.93388430 + x2 = 16.72727273 + 11.93388430 Reorder the terms: 11.93388430 + -6.909090909x + x2 = 16.72727273 + 11.93388430 Combine like terms: 16.72727273 + 11.93388430 = 28.66115703 11.93388430 + -6.909090909x + x2 = 28.66115703 Factor a perfect square on the left side: (x + -3.454545455)(x + -3.454545455) = 28.66115703 Calculate the square root of the right side: 5.353611588 Break this problem into two subproblems by setting (x + -3.454545455) equal to 5.353611588 and -5.353611588.Subproblem 1
x + -3.454545455 = 5.353611588 Simplifying x + -3.454545455 = 5.353611588 Reorder the terms: -3.454545455 + x = 5.353611588 Solving -3.454545455 + x = 5.353611588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.454545455' to each side of the equation. -3.454545455 + 3.454545455 + x = 5.353611588 + 3.454545455 Combine like terms: -3.454545455 + 3.454545455 = 0.000000000 0.000000000 + x = 5.353611588 + 3.454545455 x = 5.353611588 + 3.454545455 Combine like terms: 5.353611588 + 3.454545455 = 8.808157043 x = 8.808157043 Simplifying x = 8.808157043Subproblem 2
x + -3.454545455 = -5.353611588 Simplifying x + -3.454545455 = -5.353611588 Reorder the terms: -3.454545455 + x = -5.353611588 Solving -3.454545455 + x = -5.353611588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.454545455' to each side of the equation. -3.454545455 + 3.454545455 + x = -5.353611588 + 3.454545455 Combine like terms: -3.454545455 + 3.454545455 = 0.000000000 0.000000000 + x = -5.353611588 + 3.454545455 x = -5.353611588 + 3.454545455 Combine like terms: -5.353611588 + 3.454545455 = -1.899066133 x = -1.899066133 Simplifying x = -1.899066133Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.808157043, -1.899066133}
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