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Simplifying x2 + -2x + -60.5 = 0 Reorder the terms: -60.5 + -2x + x2 = 0 Solving -60.5 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60.5' to each side of the equation. -60.5 + -2x + 60.5 + x2 = 0 + 60.5 Reorder the terms: -60.5 + 60.5 + -2x + x2 = 0 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + -2x + x2 = 0 + 60.5 -2x + x2 = 0 + 60.5 Combine like terms: 0 + 60.5 = 60.5 -2x + x2 = 60.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 60.5 + 1 Reorder the terms: 1 + -2x + x2 = 60.5 + 1 Combine like terms: 60.5 + 1 = 61.5 1 + -2x + x2 = 61.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 61.5 Calculate the square root of the right side: 7.842193571 Break this problem into two subproblems by setting (x + -1) equal to 7.842193571 and -7.842193571.Subproblem 1
x + -1 = 7.842193571 Simplifying x + -1 = 7.842193571 Reorder the terms: -1 + x = 7.842193571 Solving -1 + x = 7.842193571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.842193571 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.842193571 + 1 x = 7.842193571 + 1 Combine like terms: 7.842193571 + 1 = 8.842193571 x = 8.842193571 Simplifying x = 8.842193571Subproblem 2
x + -1 = -7.842193571 Simplifying x + -1 = -7.842193571 Reorder the terms: -1 + x = -7.842193571 Solving -1 + x = -7.842193571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.842193571 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.842193571 + 1 x = -7.842193571 + 1 Combine like terms: -7.842193571 + 1 = -6.842193571 x = -6.842193571 Simplifying x = -6.842193571Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.842193571, -6.842193571}
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