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Simplifying x2 + -2x + -600 = 0 Reorder the terms: -600 + -2x + x2 = 0 Solving -600 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -2x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -2x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -2x + x2 = 0 + 600 -2x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -2x + x2 = 600 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 = 600 + 1 Reorder the terms: 1 + -2x + x2 = 600 + 1 Combine like terms: 600 + 1 = 601 1 + -2x + x2 = 601 Factor a perfect square on the left side: (x + -1)(x + -1) = 601 Calculate the square root of the right side: 24.515301344 Break this problem into two subproblems by setting (x + -1) equal to 24.515301344 and -24.515301344.Subproblem 1
x + -1 = 24.515301344 Simplifying x + -1 = 24.515301344 Reorder the terms: -1 + x = 24.515301344 Solving -1 + x = 24.515301344 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 = 24.515301344 + 1 Combine like terms: -1 + 1 = 0 0 + x = 24.515301344 + 1 x = 24.515301344 + 1 Combine like terms: 24.515301344 + 1 = 25.515301344 x = 25.515301344 Simplifying x = 25.515301344Subproblem 2
x + -1 = -24.515301344 Simplifying x + -1 = -24.515301344 Reorder the terms: -1 + x = -24.515301344 Solving -1 + x = -24.515301344 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 = -24.515301344 + 1 Combine like terms: -1 + 1 = 0 0 + x = -24.515301344 + 1 x = -24.515301344 + 1 Combine like terms: -24.515301344 + 1 = -23.515301344 x = -23.515301344 Simplifying x = -23.515301344Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.515301344, -23.515301344}
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