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Simplifying X(X + -1) = 206 Reorder the terms: X(-1 + X) = 206 (-1 * X + X * X) = 206 (-1X + X2) = 206 Solving -1X + X2 = 206 Solving for variable 'X'. Reorder the terms: -206 + -1X + X2 = 206 + -206 Combine like terms: 206 + -206 = 0 -206 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '206' to each side of the equation. -206 + -1X + 206 + X2 = 0 + 206 Reorder the terms: -206 + 206 + -1X + X2 = 0 + 206 Combine like terms: -206 + 206 = 0 0 + -1X + X2 = 0 + 206 -1X + X2 = 0 + 206 Combine like terms: 0 + 206 = 206 -1X + X2 = 206 The X term is -1X. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1X + 0.25 + X2 = 206 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 206 + 0.25 Combine like terms: 206 + 0.25 = 206.25 0.25 + -1X + X2 = 206.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 206.25 Calculate the square root of the right side: 14.361406616 Break this problem into two subproblems by setting (X + -0.5) equal to 14.361406616 and -14.361406616.Subproblem 1
X + -0.5 = 14.361406616 Simplifying X + -0.5 = 14.361406616 Reorder the terms: -0.5 + X = 14.361406616 Solving -0.5 + X = 14.361406616 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = 14.361406616 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 14.361406616 + 0.5 X = 14.361406616 + 0.5 Combine like terms: 14.361406616 + 0.5 = 14.861406616 X = 14.861406616 Simplifying X = 14.861406616Subproblem 2
X + -0.5 = -14.361406616 Simplifying X + -0.5 = -14.361406616 Reorder the terms: -0.5 + X = -14.361406616 Solving -0.5 + X = -14.361406616 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + X = -14.361406616 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -14.361406616 + 0.5 X = -14.361406616 + 0.5 Combine like terms: -14.361406616 + 0.5 = -13.861406616 X = -13.861406616 Simplifying X = -13.861406616Solution
The solution to the problem is based on the solutions from the subproblems. X = {14.861406616, -13.861406616}
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