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Simplifying X(X + -1) = 121 Reorder the terms: X(-1 + X) = 121 (-1 * X + X * X) = 121 (-1X + X2) = 121 Solving -1X + X2 = 121 Solving for variable 'X'. Reorder the terms: -121 + -1X + X2 = 121 + -121 Combine like terms: 121 + -121 = 0 -121 + -1X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + -1X + 121 + X2 = 0 + 121 Reorder the terms: -121 + 121 + -1X + X2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + -1X + X2 = 0 + 121 -1X + X2 = 0 + 121 Combine like terms: 0 + 121 = 121 -1X + X2 = 121 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 = 121 + 0.25 Reorder the terms: 0.25 + -1X + X2 = 121 + 0.25 Combine like terms: 121 + 0.25 = 121.25 0.25 + -1X + X2 = 121.25 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (X + -0.5) equal to 11.011357773 and -11.011357773.Subproblem 1
X + -0.5 = 11.011357773 Simplifying X + -0.5 = 11.011357773 Reorder the terms: -0.5 + X = 11.011357773 Solving -0.5 + X = 11.011357773 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 = 11.011357773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 11.011357773 + 0.5 X = 11.011357773 + 0.5 Combine like terms: 11.011357773 + 0.5 = 11.511357773 X = 11.511357773 Simplifying X = 11.511357773Subproblem 2
X + -0.5 = -11.011357773 Simplifying X + -0.5 = -11.011357773 Reorder the terms: -0.5 + X = -11.011357773 Solving -0.5 + X = -11.011357773 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 = -11.011357773 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -11.011357773 + 0.5 X = -11.011357773 + 0.5 Combine like terms: -11.011357773 + 0.5 = -10.511357773 X = -10.511357773 Simplifying X = -10.511357773Solution
The solution to the problem is based on the solutions from the subproblems. X = {11.511357773, -10.511357773}
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