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Simplifying x2 = 121x + 100 Reorder the terms: x2 = 100 + 121x Solving x2 = 100 + 121x Solving for variable 'x'. Reorder the terms: -100 + -121x + x2 = 100 + 121x + -100 + -121x Reorder the terms: -100 + -121x + x2 = 100 + -100 + 121x + -121x Combine like terms: 100 + -100 = 0 -100 + -121x + x2 = 0 + 121x + -121x -100 + -121x + x2 = 121x + -121x Combine like terms: 121x + -121x = 0 -100 + -121x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -121x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -121x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -121x + x2 = 0 + 100 -121x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -121x + x2 = 100 The x term is -121x. Take half its coefficient (-60.5). Square it (3660.25) and add it to both sides. Add '3660.25' to each side of the equation. -121x + 3660.25 + x2 = 100 + 3660.25 Reorder the terms: 3660.25 + -121x + x2 = 100 + 3660.25 Combine like terms: 100 + 3660.25 = 3760.25 3660.25 + -121x + x2 = 3760.25 Factor a perfect square on the left side: (x + -60.5)(x + -60.5) = 3760.25 Calculate the square root of the right side: 61.320877358 Break this problem into two subproblems by setting (x + -60.5) equal to 61.320877358 and -61.320877358.Subproblem 1
x + -60.5 = 61.320877358 Simplifying x + -60.5 = 61.320877358 Reorder the terms: -60.5 + x = 61.320877358 Solving -60.5 + x = 61.320877358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.5' to each side of the equation. -60.5 + 60.5 + x = 61.320877358 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = 61.320877358 + 60.5 x = 61.320877358 + 60.5 Combine like terms: 61.320877358 + 60.5 = 121.820877358 x = 121.820877358 Simplifying x = 121.820877358Subproblem 2
x + -60.5 = -61.320877358 Simplifying x + -60.5 = -61.320877358 Reorder the terms: -60.5 + x = -61.320877358 Solving -60.5 + x = -61.320877358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.5' to each side of the equation. -60.5 + 60.5 + x = -61.320877358 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = -61.320877358 + 60.5 x = -61.320877358 + 60.5 Combine like terms: -61.320877358 + 60.5 = -0.820877358 x = -0.820877358 Simplifying x = -0.820877358Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.820877358, -0.820877358}
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