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Simplifying x2 + x + -3006 = 0 Reorder the terms: -3006 + x + x2 = 0 Solving -3006 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3006' to each side of the equation. -3006 + x + 3006 + x2 = 0 + 3006 Reorder the terms: -3006 + 3006 + x + x2 = 0 + 3006 Combine like terms: -3006 + 3006 = 0 0 + x + x2 = 0 + 3006 x + x2 = 0 + 3006 Combine like terms: 0 + 3006 = 3006 x + x2 = 3006 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3006 + 0.25 Reorder the terms: 0.25 + x + x2 = 3006 + 0.25 Combine like terms: 3006 + 0.25 = 3006.25 0.25 + x + x2 = 3006.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3006.25 Calculate the square root of the right side: 54.829280499 Break this problem into two subproblems by setting (x + 0.5) equal to 54.829280499 and -54.829280499.Subproblem 1
x + 0.5 = 54.829280499 Simplifying x + 0.5 = 54.829280499 Reorder the terms: 0.5 + x = 54.829280499 Solving 0.5 + x = 54.829280499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 54.829280499 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 54.829280499 + -0.5 x = 54.829280499 + -0.5 Combine like terms: 54.829280499 + -0.5 = 54.329280499 x = 54.329280499 Simplifying x = 54.329280499Subproblem 2
x + 0.5 = -54.829280499 Simplifying x + 0.5 = -54.829280499 Reorder the terms: 0.5 + x = -54.829280499 Solving 0.5 + x = -54.829280499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -54.829280499 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -54.829280499 + -0.5 x = -54.829280499 + -0.5 Combine like terms: -54.829280499 + -0.5 = -55.329280499 x = -55.329280499 Simplifying x = -55.329280499Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.329280499, -55.329280499}
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