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Simplifying x2 + 4x + -206 = 0 Reorder the terms: -206 + 4x + x2 = 0 Solving -206 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '206' to each side of the equation. -206 + 4x + 206 + x2 = 0 + 206 Reorder the terms: -206 + 206 + 4x + x2 = 0 + 206 Combine like terms: -206 + 206 = 0 0 + 4x + x2 = 0 + 206 4x + x2 = 0 + 206 Combine like terms: 0 + 206 = 206 4x + x2 = 206 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 = 206 + 4 Reorder the terms: 4 + 4x + x2 = 206 + 4 Combine like terms: 206 + 4 = 210 4 + 4x + x2 = 210 Factor a perfect square on the left side: (x + 2)(x + 2) = 210 Calculate the square root of the right side: 14.491376746 Break this problem into two subproblems by setting (x + 2) equal to 14.491376746 and -14.491376746.Subproblem 1
x + 2 = 14.491376746 Simplifying x + 2 = 14.491376746 Reorder the terms: 2 + x = 14.491376746 Solving 2 + x = 14.491376746 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 = 14.491376746 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.491376746 + -2 x = 14.491376746 + -2 Combine like terms: 14.491376746 + -2 = 12.491376746 x = 12.491376746 Simplifying x = 12.491376746Subproblem 2
x + 2 = -14.491376746 Simplifying x + 2 = -14.491376746 Reorder the terms: 2 + x = -14.491376746 Solving 2 + x = -14.491376746 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 = -14.491376746 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.491376746 + -2 x = -14.491376746 + -2 Combine like terms: -14.491376746 + -2 = -16.491376746 x = -16.491376746 Simplifying x = -16.491376746Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.491376746, -16.491376746}
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