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Simplifying x2 + (x * 0.1) = 46 Reorder the terms for easier multiplication: x2 + (0.1x) = 46 Reorder the terms: (0.1x) + x2 = 46 Solving (0.1x) + x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + (0.1x) + x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + (0.1x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + (0.1x) + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + (0.1x) + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + (0.1x) + x2 = 0 + 46 (0.1x) + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 (0.1x) + x2 = 46 The x term is (0.1x). Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. (0.1x) + 0.0025 + x2 = 46 + 0.0025 Reorder the terms: 0.0025 + (0.1x) + x2 = 46 + 0.0025 Combine like terms: 46 + 0.0025 = 46.0025 0.0025 + (0.1x) + x2 = 46.0025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 46.0025 Calculate the square root of the right side: 6.782514283 Break this problem into two subproblems by setting (x + 0.05) equal to 6.782514283 and -6.782514283.Subproblem 1
x + 0.05 = 6.782514283 Simplifying x + 0.05 = 6.782514283 Reorder the terms: 0.05 + x = 6.782514283 Solving 0.05 + x = 6.782514283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 6.782514283 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 6.782514283 + -0.05 x = 6.782514283 + -0.05 Combine like terms: 6.782514283 + -0.05 = 6.732514283 x = 6.732514283 Simplifying x = 6.732514283Subproblem 2
x + 0.05 = -6.782514283 Simplifying x + 0.05 = -6.782514283 Reorder the terms: 0.05 + x = -6.782514283 Solving 0.05 + x = -6.782514283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -6.782514283 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -6.782514283 + -0.05 x = -6.782514283 + -0.05 Combine like terms: -6.782514283 + -0.05 = -6.832514283 x = -6.832514283 Simplifying x = -6.832514283Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.732514283, -6.832514283}
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