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Simplifying x + x + x(x + 2) = 360 Reorder the terms: x + x + x(2 + x) = 360 x + x + (2 * x + x * x) = 360 x + x + (2x + x2) = 360 Combine like terms: x + x = 2x 2x + 2x + x2 = 360 Combine like terms: 2x + 2x = 4x 4x + x2 = 360 Solving 4x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 4x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 4x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 4x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 4x + x2 = 0 + 360 4x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 4x + x2 = 360 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 360 + 4 Reorder the terms: 4 + 4x + x2 = 360 + 4 Combine like terms: 360 + 4 = 364 4 + 4x + x2 = 364 Factor a perfect square on the left side: (x + 2)(x + 2) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (x + 2) equal to 19.078784028 and -19.078784028.Subproblem 1
x + 2 = 19.078784028 Simplifying x + 2 = 19.078784028 Reorder the terms: 2 + x = 19.078784028 Solving 2 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.078784028 + -2 x = 19.078784028 + -2 Combine like terms: 19.078784028 + -2 = 17.078784028 x = 17.078784028 Simplifying x = 17.078784028Subproblem 2
x + 2 = -19.078784028 Simplifying x + 2 = -19.078784028 Reorder the terms: 2 + x = -19.078784028 Solving 2 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -19.078784028 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.078784028 + -2 x = -19.078784028 + -2 Combine like terms: -19.078784028 + -2 = -21.078784028 x = -21.078784028 Simplifying x = -21.078784028Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.078784028, -21.078784028}
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