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Simplifying -11x2 + -12x + 27 = 0 Reorder the terms: 27 + -12x + -11x2 = 0 Solving 27 + -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'. -2.454545455 + 1.090909091x + x2 = 0 Move the constant term to the right: Add '2.454545455' to each side of the equation. -2.454545455 + 1.090909091x + 2.454545455 + x2 = 0 + 2.454545455 Reorder the terms: -2.454545455 + 2.454545455 + 1.090909091x + x2 = 0 + 2.454545455 Combine like terms: -2.454545455 + 2.454545455 = 0.000000000 0.000000000 + 1.090909091x + x2 = 0 + 2.454545455 1.090909091x + x2 = 0 + 2.454545455 Combine like terms: 0 + 2.454545455 = 2.454545455 1.090909091x + x2 = 2.454545455 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 = 2.454545455 + 0.2975206612 Reorder the terms: 0.2975206612 + 1.090909091x + x2 = 2.454545455 + 0.2975206612 Combine like terms: 2.454545455 + 0.2975206612 = 2.7520661162 0.2975206612 + 1.090909091x + x2 = 2.7520661162 Factor a perfect square on the left side: (x + 0.5454545455)(x + 0.5454545455) = 2.7520661162 Calculate the square root of the right side: 1.658935236 Break this problem into two subproblems by setting (x + 0.5454545455) equal to 1.658935236 and -1.658935236.Subproblem 1
x + 0.5454545455 = 1.658935236 Simplifying x + 0.5454545455 = 1.658935236 Reorder the terms: 0.5454545455 + x = 1.658935236 Solving 0.5454545455 + x = 1.658935236 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 = 1.658935236 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = 1.658935236 + -0.5454545455 x = 1.658935236 + -0.5454545455 Combine like terms: 1.658935236 + -0.5454545455 = 1.1134806905 x = 1.1134806905 Simplifying x = 1.1134806905Subproblem 2
x + 0.5454545455 = -1.658935236 Simplifying x + 0.5454545455 = -1.658935236 Reorder the terms: 0.5454545455 + x = -1.658935236 Solving 0.5454545455 + x = -1.658935236 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 = -1.658935236 + -0.5454545455 Combine like terms: 0.5454545455 + -0.5454545455 = 0.0000000000 0.0000000000 + x = -1.658935236 + -0.5454545455 x = -1.658935236 + -0.5454545455 Combine like terms: -1.658935236 + -0.5454545455 = -2.2043897815 x = -2.2043897815 Simplifying x = -2.2043897815Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1134806905, -2.2043897815}
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