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Simplifying x2 + -2x + -460 = 0 Reorder the terms: -460 + -2x + x2 = 0 Solving -460 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '460' to each side of the equation. -460 + -2x + 460 + x2 = 0 + 460 Reorder the terms: -460 + 460 + -2x + x2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + -2x + x2 = 0 + 460 -2x + x2 = 0 + 460 Combine like terms: 0 + 460 = 460 -2x + x2 = 460 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 = 460 + 1 Reorder the terms: 1 + -2x + x2 = 460 + 1 Combine like terms: 460 + 1 = 461 1 + -2x + x2 = 461 Factor a perfect square on the left side: (x + -1)(x + -1) = 461 Calculate the square root of the right side: 21.470910554 Break this problem into two subproblems by setting (x + -1) equal to 21.470910554 and -21.470910554.Subproblem 1
x + -1 = 21.470910554 Simplifying x + -1 = 21.470910554 Reorder the terms: -1 + x = 21.470910554 Solving -1 + x = 21.470910554 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 = 21.470910554 + 1 Combine like terms: -1 + 1 = 0 0 + x = 21.470910554 + 1 x = 21.470910554 + 1 Combine like terms: 21.470910554 + 1 = 22.470910554 x = 22.470910554 Simplifying x = 22.470910554Subproblem 2
x + -1 = -21.470910554 Simplifying x + -1 = -21.470910554 Reorder the terms: -1 + x = -21.470910554 Solving -1 + x = -21.470910554 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 = -21.470910554 + 1 Combine like terms: -1 + 1 = 0 0 + x = -21.470910554 + 1 x = -21.470910554 + 1 Combine like terms: -21.470910554 + 1 = -20.470910554 x = -20.470910554 Simplifying x = -20.470910554Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.470910554, -20.470910554}
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