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Simplifying 11x2 + -12x + -10 = 0 Reorder the terms: -10 + -12x + 11x2 = 0 Solving -10 + -12x + 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'. -0.9090909091 + -1.090909091x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -1.090909091x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -1.090909091x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -1.090909091x + x2 = 0 + 0.9090909091 -1.090909091x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -1.090909091x + x2 = 0.9090909091 The x term is -1.090909091x. Take half its coefficient (-0.5454545455). Square it (0.2975206612) and add it to both sides. Add '0.2975206612' to each side of the equation. -1.090909091x + 0.2975206612 + x2 = 0.9090909091 + 0.2975206612 Reorder the terms: 0.2975206612 + -1.090909091x + x2 = 0.9090909091 + 0.2975206612 Combine like terms: 0.9090909091 + 0.2975206612 = 1.2066115703 0.2975206612 + -1.090909091x + x2 = 1.2066115703 Factor a perfect square on the left side: (x + -0.5454545455)(x + -0.5454545455) = 1.2066115703 Calculate the square root of the right side: 1.098458725 Break this problem into two subproblems by setting (x + -0.5454545455) equal to 1.098458725 and -1.098458725.Subproblem 1
x + -0.5454545455 = 1.098458725 Simplifying x + -0.5454545455 = 1.098458725 Reorder the terms: -0.5454545455 + x = 1.098458725 Solving -0.5454545455 + x = 1.098458725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = 1.098458725 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = 1.098458725 + 0.5454545455 x = 1.098458725 + 0.5454545455 Combine like terms: 1.098458725 + 0.5454545455 = 1.6439132705 x = 1.6439132705 Simplifying x = 1.6439132705Subproblem 2
x + -0.5454545455 = -1.098458725 Simplifying x + -0.5454545455 = -1.098458725 Reorder the terms: -0.5454545455 + x = -1.098458725 Solving -0.5454545455 + x = -1.098458725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5454545455' to each side of the equation. -0.5454545455 + 0.5454545455 + x = -1.098458725 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + x = -1.098458725 + 0.5454545455 x = -1.098458725 + 0.5454545455 Combine like terms: -1.098458725 + 0.5454545455 = -0.5530041795 x = -0.5530041795 Simplifying x = -0.5530041795Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6439132705, -0.5530041795}
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