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Simplifying 0.10x(x + 100) + 0.10x = 11 Reorder the terms: 0.10x(100 + x) + 0.10x = 11 (100 * 0.10x + x * 0.10x) + 0.10x = 11 (10x + 0.10x2) + 0.10x = 11 Reorder the terms: 10x + 0.10x + 0.10x2 = 11 Combine like terms: 10x + 0.10x = 10.1x 10.1x + 0.10x2 = 11 Solving 10.1x + 0.10x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 10.1x + 0.10x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 10.1x + 0.10x2 = 0 Begin completing the square. Divide all terms by 0.10 the coefficient of the squared term: Divide each side by '0.10'. -110 + 101x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + 101x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 101x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 101x + x2 = 0 + 110 101x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 101x + x2 = 110 The x term is 101x. Take half its coefficient (50.5). Square it (2550.25) and add it to both sides. Add '2550.25' to each side of the equation. 101x + 2550.25 + x2 = 110 + 2550.25 Reorder the terms: 2550.25 + 101x + x2 = 110 + 2550.25 Combine like terms: 110 + 2550.25 = 2660.25 2550.25 + 101x + x2 = 2660.25 Factor a perfect square on the left side: (x + 50.5)(x + 50.5) = 2660.25 Calculate the square root of the right side: 51.577611422 Break this problem into two subproblems by setting (x + 50.5) equal to 51.577611422 and -51.577611422.Subproblem 1
x + 50.5 = 51.577611422 Simplifying x + 50.5 = 51.577611422 Reorder the terms: 50.5 + x = 51.577611422 Solving 50.5 + x = 51.577611422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = 51.577611422 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = 51.577611422 + -50.5 x = 51.577611422 + -50.5 Combine like terms: 51.577611422 + -50.5 = 1.077611422 x = 1.077611422 Simplifying x = 1.077611422Subproblem 2
x + 50.5 = -51.577611422 Simplifying x + 50.5 = -51.577611422 Reorder the terms: 50.5 + x = -51.577611422 Solving 50.5 + x = -51.577611422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = -51.577611422 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = -51.577611422 + -50.5 x = -51.577611422 + -50.5 Combine like terms: -51.577611422 + -50.5 = -102.077611422 x = -102.077611422 Simplifying x = -102.077611422Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.077611422, -102.077611422}
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