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Simplifying x2 + -5x + -3000 = 0 Reorder the terms: -3000 + -5x + x2 = 0 Solving -3000 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3000' to each side of the equation. -3000 + -5x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + -5x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + -5x + x2 = 0 + 3000 -5x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 -5x + x2 = 3000 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 3000 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 3000 + 6.25 Combine like terms: 3000 + 6.25 = 3006.25 6.25 + -5x + x2 = 3006.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3006.25 Calculate the square root of the right side: 54.829280499 Break this problem into two subproblems by setting (x + -2.5) equal to 54.829280499 and -54.829280499.Subproblem 1
x + -2.5 = 54.829280499 Simplifying x + -2.5 = 54.829280499 Reorder the terms: -2.5 + x = 54.829280499 Solving -2.5 + x = 54.829280499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 54.829280499 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 54.829280499 + 2.5 x = 54.829280499 + 2.5 Combine like terms: 54.829280499 + 2.5 = 57.329280499 x = 57.329280499 Simplifying x = 57.329280499Subproblem 2
x + -2.5 = -54.829280499 Simplifying x + -2.5 = -54.829280499 Reorder the terms: -2.5 + x = -54.829280499 Solving -2.5 + x = -54.829280499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -54.829280499 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -54.829280499 + 2.5 x = -54.829280499 + 2.5 Combine like terms: -54.829280499 + 2.5 = -52.329280499 x = -52.329280499 Simplifying x = -52.329280499Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.329280499, -52.329280499}
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