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Simplifying x2 + x + -3000 = 0 Reorder the terms: -3000 + x + x2 = 0 Solving -3000 + x + 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 + x + 3000 + x2 = 0 + 3000 Reorder the terms: -3000 + 3000 + x + x2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + x + x2 = 0 + 3000 x + x2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 x + x2 = 3000 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 = 3000 + 0.25 Reorder the terms: 0.25 + x + x2 = 3000 + 0.25 Combine like terms: 3000 + 0.25 = 3000.25 0.25 + x + x2 = 3000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3000.25 Calculate the square root of the right side: 54.77453788 Break this problem into two subproblems by setting (x + 0.5) equal to 54.77453788 and -54.77453788.Subproblem 1
x + 0.5 = 54.77453788 Simplifying x + 0.5 = 54.77453788 Reorder the terms: 0.5 + x = 54.77453788 Solving 0.5 + x = 54.77453788 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 = 54.77453788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 54.77453788 + -0.5 x = 54.77453788 + -0.5 Combine like terms: 54.77453788 + -0.5 = 54.27453788 x = 54.27453788 Simplifying x = 54.27453788Subproblem 2
x + 0.5 = -54.77453788 Simplifying x + 0.5 = -54.77453788 Reorder the terms: 0.5 + x = -54.77453788 Solving 0.5 + x = -54.77453788 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 = -54.77453788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -54.77453788 + -0.5 x = -54.77453788 + -0.5 Combine like terms: -54.77453788 + -0.5 = -55.27453788 x = -55.27453788 Simplifying x = -55.27453788Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.27453788, -55.27453788}
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