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Simplifying 11x2 + -440x + 2529 = 0 Reorder the terms: 2529 + -440x + 11x2 = 0 Solving 2529 + -440x + 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'. 229.9090909 + -40x + x2 = 0 Move the constant term to the right: Add '-229.9090909' to each side of the equation. 229.9090909 + -40x + -229.9090909 + x2 = 0 + -229.9090909 Reorder the terms: 229.9090909 + -229.9090909 + -40x + x2 = 0 + -229.9090909 Combine like terms: 229.9090909 + -229.9090909 = 0.0000000 0.0000000 + -40x + x2 = 0 + -229.9090909 -40x + x2 = 0 + -229.9090909 Combine like terms: 0 + -229.9090909 = -229.9090909 -40x + x2 = -229.9090909 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -229.9090909 + 400 Reorder the terms: 400 + -40x + x2 = -229.9090909 + 400 Combine like terms: -229.9090909 + 400 = 170.0909091 400 + -40x + x2 = 170.0909091 Factor a perfect square on the left side: (x + -20)(x + -20) = 170.0909091 Calculate the square root of the right side: 13.041890549 Break this problem into two subproblems by setting (x + -20) equal to 13.041890549 and -13.041890549.Subproblem 1
x + -20 = 13.041890549 Simplifying x + -20 = 13.041890549 Reorder the terms: -20 + x = 13.041890549 Solving -20 + x = 13.041890549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 13.041890549 + 20 Combine like terms: -20 + 20 = 0 0 + x = 13.041890549 + 20 x = 13.041890549 + 20 Combine like terms: 13.041890549 + 20 = 33.041890549 x = 33.041890549 Simplifying x = 33.041890549Subproblem 2
x + -20 = -13.041890549 Simplifying x + -20 = -13.041890549 Reorder the terms: -20 + x = -13.041890549 Solving -20 + x = -13.041890549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -13.041890549 + 20 Combine like terms: -20 + 20 = 0 0 + x = -13.041890549 + 20 x = -13.041890549 + 20 Combine like terms: -13.041890549 + 20 = 6.958109451 x = 6.958109451 Simplifying x = 6.958109451Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.041890549, 6.958109451}
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