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Simplifying 0.1(x + 100) * 1.1x = 46 Reorder the terms: 0.1(100 + x) * 1.1x = 46 Reorder the terms for easier multiplication: 0.1 * 1.1x(100 + x) = 46 Multiply 0.1 * 1.1 0.11x(100 + x) = 46 (100 * 0.11x + x * 0.11x) = 46 (11x + 0.11x2) = 46 Solving 11x + 0.11x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 11x + 0.11x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 11x + 0.11x2 = 0 Begin completing the square. Divide all terms by 0.11 the coefficient of the squared term: Divide each side by '0.11'. -418.1818182 + 100x + x2 = 0 Move the constant term to the right: Add '418.1818182' to each side of the equation. -418.1818182 + 100x + 418.1818182 + x2 = 0 + 418.1818182 Reorder the terms: -418.1818182 + 418.1818182 + 100x + x2 = 0 + 418.1818182 Combine like terms: -418.1818182 + 418.1818182 = 0.0000000 0.0000000 + 100x + x2 = 0 + 418.1818182 100x + x2 = 0 + 418.1818182 Combine like terms: 0 + 418.1818182 = 418.1818182 100x + x2 = 418.1818182 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 418.1818182 + 2500 Reorder the terms: 2500 + 100x + x2 = 418.1818182 + 2500 Combine like terms: 418.1818182 + 2500 = 2918.1818182 2500 + 100x + x2 = 2918.1818182 Factor a perfect square on the left side: (x + 50)(x + 50) = 2918.1818182 Calculate the square root of the right side: 54.020198243 Break this problem into two subproblems by setting (x + 50) equal to 54.020198243 and -54.020198243.Subproblem 1
x + 50 = 54.020198243 Simplifying x + 50 = 54.020198243 Reorder the terms: 50 + x = 54.020198243 Solving 50 + x = 54.020198243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 54.020198243 + -50 Combine like terms: 50 + -50 = 0 0 + x = 54.020198243 + -50 x = 54.020198243 + -50 Combine like terms: 54.020198243 + -50 = 4.020198243 x = 4.020198243 Simplifying x = 4.020198243Subproblem 2
x + 50 = -54.020198243 Simplifying x + 50 = -54.020198243 Reorder the terms: 50 + x = -54.020198243 Solving 50 + x = -54.020198243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -54.020198243 + -50 Combine like terms: 50 + -50 = 0 0 + x = -54.020198243 + -50 x = -54.020198243 + -50 Combine like terms: -54.020198243 + -50 = -104.020198243 x = -104.020198243 Simplifying x = -104.020198243Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.020198243, -104.020198243}
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