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Simplifying 11x2 + x + -400 = 0 Reorder the terms: -400 + x + 11x2 = 0 Solving -400 + x + 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'. -36.36363636 + 0.09090909091x + x2 = 0 Move the constant term to the right: Add '36.36363636' to each side of the equation. -36.36363636 + 0.09090909091x + 36.36363636 + x2 = 0 + 36.36363636 Reorder the terms: -36.36363636 + 36.36363636 + 0.09090909091x + x2 = 0 + 36.36363636 Combine like terms: -36.36363636 + 36.36363636 = 0.00000000 0.00000000 + 0.09090909091x + x2 = 0 + 36.36363636 0.09090909091x + x2 = 0 + 36.36363636 Combine like terms: 0 + 36.36363636 = 36.36363636 0.09090909091x + x2 = 36.36363636 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.09090909091x + 0.25 + x2 = 36.36363636 + 0.25 Reorder the terms: 0.25 + 0.09090909091x + x2 = 36.36363636 + 0.25 Combine like terms: 36.36363636 + 0.25 = 36.61363636 0.25 + 0.09090909091x + x2 = 36.61363636 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 36.61363636 Calculate the square root of the right side: 6.05092029 Break this problem into two subproblems by setting (x + 0.5) equal to 6.05092029 and -6.05092029.Subproblem 1
x + 0.5 = 6.05092029 Simplifying x + 0.5 = 6.05092029 Reorder the terms: 0.5 + x = 6.05092029 Solving 0.5 + x = 6.05092029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.05092029 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.05092029 + -0.5 x = 6.05092029 + -0.5 Combine like terms: 6.05092029 + -0.5 = 5.55092029 x = 5.55092029 Simplifying x = 5.55092029Subproblem 2
x + 0.5 = -6.05092029 Simplifying x + 0.5 = -6.05092029 Reorder the terms: 0.5 + x = -6.05092029 Solving 0.5 + x = -6.05092029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.05092029 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.05092029 + -0.5 x = -6.05092029 + -0.5 Combine like terms: -6.05092029 + -0.5 = -6.55092029 x = -6.55092029 Simplifying x = -6.55092029Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.55092029, -6.55092029}
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