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Simplifying x2 + -121x + 85 = 0 Reorder the terms: 85 + -121x + x2 = 0 Solving 85 + -121x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-85' to each side of the equation. 85 + -121x + -85 + x2 = 0 + -85 Reorder the terms: 85 + -85 + -121x + x2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + -121x + x2 = 0 + -85 -121x + x2 = 0 + -85 Combine like terms: 0 + -85 = -85 -121x + x2 = -85 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 = -85 + 3660.25 Reorder the terms: 3660.25 + -121x + x2 = -85 + 3660.25 Combine like terms: -85 + 3660.25 = 3575.25 3660.25 + -121x + x2 = 3575.25 Factor a perfect square on the left side: (x + -60.5)(x + -60.5) = 3575.25 Calculate the square root of the right side: 59.793394284 Break this problem into two subproblems by setting (x + -60.5) equal to 59.793394284 and -59.793394284.Subproblem 1
x + -60.5 = 59.793394284 Simplifying x + -60.5 = 59.793394284 Reorder the terms: -60.5 + x = 59.793394284 Solving -60.5 + x = 59.793394284 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 = 59.793394284 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = 59.793394284 + 60.5 x = 59.793394284 + 60.5 Combine like terms: 59.793394284 + 60.5 = 120.293394284 x = 120.293394284 Simplifying x = 120.293394284Subproblem 2
x + -60.5 = -59.793394284 Simplifying x + -60.5 = -59.793394284 Reorder the terms: -60.5 + x = -59.793394284 Solving -60.5 + x = -59.793394284 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 = -59.793394284 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = -59.793394284 + 60.5 x = -59.793394284 + 60.5 Combine like terms: -59.793394284 + 60.5 = 0.706605716 x = 0.706605716 Simplifying x = 0.706605716Solution
The solution to the problem is based on the solutions from the subproblems. x = {120.293394284, 0.706605716}
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