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Simplifying x2 + x * 0.2 = 120 Reorder the terms for easier multiplication: x2 + 0.2x = 120 Reorder the terms: 0.2x + x2 = 120 Solving 0.2x + x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 0.2x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 0.2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 0.2x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 0.2x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 0.2x + x2 = 0 + 120 0.2x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 0.2x + x2 = 120 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 120 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 120 + 0.01 Combine like terms: 120 + 0.01 = 120.01 0.01 + 0.2x + x2 = 120.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 120.01 Calculate the square root of the right side: 10.954907576 Break this problem into two subproblems by setting (x + 0.1) equal to 10.954907576 and -10.954907576.Subproblem 1
x + 0.1 = 10.954907576 Simplifying x + 0.1 = 10.954907576 Reorder the terms: 0.1 + x = 10.954907576 Solving 0.1 + x = 10.954907576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 10.954907576 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 10.954907576 + -0.1 x = 10.954907576 + -0.1 Combine like terms: 10.954907576 + -0.1 = 10.854907576 x = 10.854907576 Simplifying x = 10.854907576Subproblem 2
x + 0.1 = -10.954907576 Simplifying x + 0.1 = -10.954907576 Reorder the terms: 0.1 + x = -10.954907576 Solving 0.1 + x = -10.954907576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -10.954907576 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -10.954907576 + -0.1 x = -10.954907576 + -0.1 Combine like terms: -10.954907576 + -0.1 = -11.054907576 x = -11.054907576 Simplifying x = -11.054907576Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.854907576, -11.054907576}
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