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Simplifying 11x2 + -23x + -21 = 0 Reorder the terms: -21 + -23x + 11x2 = 0 Solving -21 + -23x + 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'. -1.909090909 + -2.090909091x + x2 = 0 Move the constant term to the right: Add '1.909090909' to each side of the equation. -1.909090909 + -2.090909091x + 1.909090909 + x2 = 0 + 1.909090909 Reorder the terms: -1.909090909 + 1.909090909 + -2.090909091x + x2 = 0 + 1.909090909 Combine like terms: -1.909090909 + 1.909090909 = 0.000000000 0.000000000 + -2.090909091x + x2 = 0 + 1.909090909 -2.090909091x + x2 = 0 + 1.909090909 Combine like terms: 0 + 1.909090909 = 1.909090909 -2.090909091x + x2 = 1.909090909 The x term is -2.090909091x. Take half its coefficient (-1.045454546). Square it (1.092975208) and add it to both sides. Add '1.092975208' to each side of the equation. -2.090909091x + 1.092975208 + x2 = 1.909090909 + 1.092975208 Reorder the terms: 1.092975208 + -2.090909091x + x2 = 1.909090909 + 1.092975208 Combine like terms: 1.909090909 + 1.092975208 = 3.002066117 1.092975208 + -2.090909091x + x2 = 3.002066117 Factor a perfect square on the left side: (x + -1.045454546)(x + -1.045454546) = 3.002066117 Calculate the square root of the right side: 1.732647142 Break this problem into two subproblems by setting (x + -1.045454546) equal to 1.732647142 and -1.732647142.Subproblem 1
x + -1.045454546 = 1.732647142 Simplifying x + -1.045454546 = 1.732647142 Reorder the terms: -1.045454546 + x = 1.732647142 Solving -1.045454546 + x = 1.732647142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.045454546' to each side of the equation. -1.045454546 + 1.045454546 + x = 1.732647142 + 1.045454546 Combine like terms: -1.045454546 + 1.045454546 = 0.000000000 0.000000000 + x = 1.732647142 + 1.045454546 x = 1.732647142 + 1.045454546 Combine like terms: 1.732647142 + 1.045454546 = 2.778101688 x = 2.778101688 Simplifying x = 2.778101688Subproblem 2
x + -1.045454546 = -1.732647142 Simplifying x + -1.045454546 = -1.732647142 Reorder the terms: -1.045454546 + x = -1.732647142 Solving -1.045454546 + x = -1.732647142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.045454546' to each side of the equation. -1.045454546 + 1.045454546 + x = -1.732647142 + 1.045454546 Combine like terms: -1.045454546 + 1.045454546 = 0.000000000 0.000000000 + x = -1.732647142 + 1.045454546 x = -1.732647142 + 1.045454546 Combine like terms: -1.732647142 + 1.045454546 = -0.687192596 x = -0.687192596 Simplifying x = -0.687192596Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.778101688, -0.687192596}
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