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Simplifying (X + 22)(X + 22) + 2X = 360 Reorder the terms: (22 + X)(X + 22) + 2X = 360 Reorder the terms: (22 + X)(22 + X) + 2X = 360 Multiply (22 + X) * (22 + X) (22(22 + X) + X(22 + X)) + 2X = 360 ((22 * 22 + X * 22) + X(22 + X)) + 2X = 360 ((484 + 22X) + X(22 + X)) + 2X = 360 (484 + 22X + (22 * X + X * X)) + 2X = 360 (484 + 22X + (22X + X2)) + 2X = 360 Combine like terms: 22X + 22X = 44X (484 + 44X + X2) + 2X = 360 Reorder the terms: 484 + 44X + 2X + X2 = 360 Combine like terms: 44X + 2X = 46X 484 + 46X + X2 = 360 Solving 484 + 46X + X2 = 360 Solving for variable 'X'. Reorder the terms: 484 + -360 + 46X + X2 = 360 + -360 Combine like terms: 484 + -360 = 124 124 + 46X + X2 = 360 + -360 Combine like terms: 360 + -360 = 0 124 + 46X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + 46X + -124 + X2 = 0 + -124 Reorder the terms: 124 + -124 + 46X + X2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + 46X + X2 = 0 + -124 46X + X2 = 0 + -124 Combine like terms: 0 + -124 = -124 46X + X2 = -124 The X term is 46X. Take half its coefficient (23). Square it (529) and add it to both sides. Add '529' to each side of the equation. 46X + 529 + X2 = -124 + 529 Reorder the terms: 529 + 46X + X2 = -124 + 529 Combine like terms: -124 + 529 = 405 529 + 46X + X2 = 405 Factor a perfect square on the left side: (X + 23)(X + 23) = 405 Calculate the square root of the right side: 20.124611797 Break this problem into two subproblems by setting (X + 23) equal to 20.124611797 and -20.124611797.Subproblem 1
X + 23 = 20.124611797 Simplifying X + 23 = 20.124611797 Reorder the terms: 23 + X = 20.124611797 Solving 23 + X = 20.124611797 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + X = 20.124611797 + -23 Combine like terms: 23 + -23 = 0 0 + X = 20.124611797 + -23 X = 20.124611797 + -23 Combine like terms: 20.124611797 + -23 = -2.875388203 X = -2.875388203 Simplifying X = -2.875388203Subproblem 2
X + 23 = -20.124611797 Simplifying X + 23 = -20.124611797 Reorder the terms: 23 + X = -20.124611797 Solving 23 + X = -20.124611797 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + X = -20.124611797 + -23 Combine like terms: 23 + -23 = 0 0 + X = -20.124611797 + -23 X = -20.124611797 + -23 Combine like terms: -20.124611797 + -23 = -43.124611797 X = -43.124611797 Simplifying X = -43.124611797Solution
The solution to the problem is based on the solutions from the subproblems. X = {-2.875388203, -43.124611797}
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