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Simplifying x2 + 2x = 198 Reorder the terms: 2x + x2 = 198 Solving 2x + x2 = 198 Solving for variable 'x'. Reorder the terms: -198 + 2x + x2 = 198 + -198 Combine like terms: 198 + -198 = 0 -198 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 2x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 2x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 2x + x2 = 0 + 198 2x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 2x + x2 = 198 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 198 + 1 Reorder the terms: 1 + 2x + x2 = 198 + 1 Combine like terms: 198 + 1 = 199 1 + 2x + x2 = 199 Factor a perfect square on the left side: (x + 1)(x + 1) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (x + 1) equal to 14.10673598 and -14.10673598.Subproblem 1
x + 1 = 14.10673598 Simplifying x + 1 = 14.10673598 Reorder the terms: 1 + x = 14.10673598 Solving 1 + x = 14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 14.10673598 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.10673598 + -1 x = 14.10673598 + -1 Combine like terms: 14.10673598 + -1 = 13.10673598 x = 13.10673598 Simplifying x = 13.10673598Subproblem 2
x + 1 = -14.10673598 Simplifying x + 1 = -14.10673598 Reorder the terms: 1 + x = -14.10673598 Solving 1 + x = -14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -14.10673598 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.10673598 + -1 x = -14.10673598 + -1 Combine like terms: -14.10673598 + -1 = -15.10673598 x = -15.10673598 Simplifying x = -15.10673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.10673598, -15.10673598}
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