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Simplifying x2 + 4x = 198 Reorder the terms: 4x + x2 = 198 Solving 4x + x2 = 198 Solving for variable 'x'. Reorder the terms: -198 + 4x + x2 = 198 + -198 Combine like terms: 198 + -198 = 0 -198 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 4x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 4x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 4x + x2 = 0 + 198 4x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 4x + x2 = 198 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 = 198 + 4 Reorder the terms: 4 + 4x + x2 = 198 + 4 Combine like terms: 198 + 4 = 202 4 + 4x + x2 = 202 Factor a perfect square on the left side: (x + 2)(x + 2) = 202 Calculate the square root of the right side: 14.212670404 Break this problem into two subproblems by setting (x + 2) equal to 14.212670404 and -14.212670404.Subproblem 1
x + 2 = 14.212670404 Simplifying x + 2 = 14.212670404 Reorder the terms: 2 + x = 14.212670404 Solving 2 + x = 14.212670404 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 = 14.212670404 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.212670404 + -2 x = 14.212670404 + -2 Combine like terms: 14.212670404 + -2 = 12.212670404 x = 12.212670404 Simplifying x = 12.212670404Subproblem 2
x + 2 = -14.212670404 Simplifying x + 2 = -14.212670404 Reorder the terms: 2 + x = -14.212670404 Solving 2 + x = -14.212670404 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 = -14.212670404 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.212670404 + -2 x = -14.212670404 + -2 Combine like terms: -14.212670404 + -2 = -16.212670404 x = -16.212670404 Simplifying x = -16.212670404Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.212670404, -16.212670404}
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