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Simplifying x2 + -11x + 0.1 = 0 Reorder the terms: 0.1 + -11x + x2 = 0 Solving 0.1 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -11x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + -11x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -11x + x2 = 0 + -0.1 -11x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 -11x + x2 = -0.1 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -0.1 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -0.1 + 30.25 Combine like terms: -0.1 + 30.25 = 30.15 30.25 + -11x + x2 = 30.15 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 30.15 Calculate the square root of the right side: 5.490901565 Break this problem into two subproblems by setting (x + -5.5) equal to 5.490901565 and -5.490901565.Subproblem 1
x + -5.5 = 5.490901565 Simplifying x + -5.5 = 5.490901565 Reorder the terms: -5.5 + x = 5.490901565 Solving -5.5 + x = 5.490901565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.490901565 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.490901565 + 5.5 x = 5.490901565 + 5.5 Combine like terms: 5.490901565 + 5.5 = 10.990901565 x = 10.990901565 Simplifying x = 10.990901565Subproblem 2
x + -5.5 = -5.490901565 Simplifying x + -5.5 = -5.490901565 Reorder the terms: -5.5 + x = -5.490901565 Solving -5.5 + x = -5.490901565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.490901565 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.490901565 + 5.5 x = -5.490901565 + 5.5 Combine like terms: -5.490901565 + 5.5 = 0.009098435 x = 0.009098435 Simplifying x = 0.009098435Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.990901565, 0.009098435}
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