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Simplifying x + x + x + x(x + 2) = 360 Reorder the terms: x + x + x + x(2 + x) = 360 x + x + x + (2 * x + x * x) = 360 x + x + x + (2x + x2) = 360 Combine like terms: x + x = 2x 2x + x + 2x + x2 = 360 Combine like terms: 2x + x = 3x 3x + 2x + x2 = 360 Combine like terms: 3x + 2x = 5x 5x + x2 = 360 Solving 5x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 5x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 5x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 5x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 5x + x2 = 0 + 360 5x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 5x + x2 = 360 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 360 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 360 + 6.25 Combine like terms: 360 + 6.25 = 366.25 6.25 + 5x + x2 = 366.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 366.25 Calculate the square root of the right side: 19.137659209 Break this problem into two subproblems by setting (x + 2.5) equal to 19.137659209 and -19.137659209.Subproblem 1
x + 2.5 = 19.137659209 Simplifying x + 2.5 = 19.137659209 Reorder the terms: 2.5 + x = 19.137659209 Solving 2.5 + x = 19.137659209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 19.137659209 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 19.137659209 + -2.5 x = 19.137659209 + -2.5 Combine like terms: 19.137659209 + -2.5 = 16.637659209 x = 16.637659209 Simplifying x = 16.637659209Subproblem 2
x + 2.5 = -19.137659209 Simplifying x + 2.5 = -19.137659209 Reorder the terms: 2.5 + x = -19.137659209 Solving 2.5 + x = -19.137659209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -19.137659209 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -19.137659209 + -2.5 x = -19.137659209 + -2.5 Combine like terms: -19.137659209 + -2.5 = -21.637659209 x = -21.637659209 Simplifying x = -21.637659209Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.637659209, -21.637659209}
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