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Simplifying x + x + 0.4x + (x + 0.5x) + 0.5x((x + 0.5x) + 0.5x) + 0.75x = 360 Combine like terms: x + 0.5x = 1.5x x + x + 0.4x + (1.5x) + 0.5x((x + 0.5x) + 0.5x) + 0.75x = 360 x + x + 0.4x + (1.5x) + 0.5x((x + 0.5x) + 0.5x) + 0.75x = 360 Combine like terms: x + 0.5x = 1.5x x + x + 0.4x + (1.5x) + 0.5x((1.5x) + 0.5x) + 0.75x = 360 x + x + 0.4x + (1.5x) + 0.5x((1.5x) + 0.5x) + 0.75x = 360 Combine like terms: (1.5x) + 0.5x = 2x x + x + 0.4x + (1.5x) + 0.5x(2x) + 0.75x = 360 Remove parenthesis around (2x) x + x + 0.4x + (1.5x) + 0.5x * 2x + 0.75x = 360 Reorder the terms for easier multiplication: x + x + 0.4x + (1.5x) + 0.5 * 2x * x + 0.75x = 360 Multiply 0.5 * 2 x + x + 0.4x + (1.5x) + 1x * x + 0.75x = 360 Multiply x * x x + x + 0.4x + (1.5x) + 1x2 + 0.75x = 360 Reorder the terms: x + x + 0.4x + (1.5x) + 0.75x + 1x2 = 360 Combine like terms: x + x = 2x 2x + 0.4x + (1.5x) + 0.75x + 1x2 = 360 Combine like terms: 2x + 0.4x = 2.4x 2.4x + (1.5x) + 0.75x + 1x2 = 360 Combine like terms: 2.4x + (1.5x) = 3.9x 3.9x + 0.75x + 1x2 = 360 Combine like terms: 3.9x + 0.75x = 4.65x 4.65x + 1x2 = 360 Solving 4.65x + 1x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 4.65x + 1x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 4.65x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 4.65x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 4.65x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 4.65x + x2 = 0 + 360 4.65x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 4.65x + x2 = 360 The x term is 4.65x. Take half its coefficient (2.325). Square it (5.405625) and add it to both sides. Add '5.405625' to each side of the equation. 4.65x + 5.405625 + x2 = 360 + 5.405625 Reorder the terms: 5.405625 + 4.65x + x2 = 360 + 5.405625 Combine like terms: 360 + 5.405625 = 365.405625 5.405625 + 4.65x + x2 = 365.405625 Factor a perfect square on the left side: (x + 2.325)(x + 2.325) = 365.405625 Calculate the square root of the right side: 19.115585918 Break this problem into two subproblems by setting (x + 2.325) equal to 19.115585918 and -19.115585918.Subproblem 1
x + 2.325 = 19.115585918 Simplifying x + 2.325 = 19.115585918 Reorder the terms: 2.325 + x = 19.115585918 Solving 2.325 + x = 19.115585918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.325' to each side of the equation. 2.325 + -2.325 + x = 19.115585918 + -2.325 Combine like terms: 2.325 + -2.325 = 0.000 0.000 + x = 19.115585918 + -2.325 x = 19.115585918 + -2.325 Combine like terms: 19.115585918 + -2.325 = 16.790585918 x = 16.790585918 Simplifying x = 16.790585918Subproblem 2
x + 2.325 = -19.115585918 Simplifying x + 2.325 = -19.115585918 Reorder the terms: 2.325 + x = -19.115585918 Solving 2.325 + x = -19.115585918 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.325' to each side of the equation. 2.325 + -2.325 + x = -19.115585918 + -2.325 Combine like terms: 2.325 + -2.325 = 0.000 0.000 + x = -19.115585918 + -2.325 x = -19.115585918 + -2.325 Combine like terms: -19.115585918 + -2.325 = -21.440585918 x = -21.440585918 Simplifying x = -21.440585918Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.790585918, -21.440585918}
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