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Simplifying 2x2 + x + -1750 = 0 Reorder the terms: -1750 + x + 2x2 = 0 Solving -1750 + x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -875 + 0.5x + x2 = 0 Move the constant term to the right: Add '875' to each side of the equation. -875 + 0.5x + 875 + x2 = 0 + 875 Reorder the terms: -875 + 875 + 0.5x + x2 = 0 + 875 Combine like terms: -875 + 875 = 0 0 + 0.5x + x2 = 0 + 875 0.5x + x2 = 0 + 875 Combine like terms: 0 + 875 = 875 0.5x + x2 = 875 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. 0.5x + 0.25 + x2 = 875 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 875 + 0.25 Combine like terms: 875 + 0.25 = 875.25 0.25 + 0.5x + x2 = 875.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 875.25 Calculate the square root of the right side: 29.584624385 Break this problem into two subproblems by setting (x + 0.5) equal to 29.584624385 and -29.584624385.Subproblem 1
x + 0.5 = 29.584624385 Simplifying x + 0.5 = 29.584624385 Reorder the terms: 0.5 + x = 29.584624385 Solving 0.5 + x = 29.584624385 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 = 29.584624385 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 29.584624385 + -0.5 x = 29.584624385 + -0.5 Combine like terms: 29.584624385 + -0.5 = 29.084624385 x = 29.084624385 Simplifying x = 29.084624385Subproblem 2
x + 0.5 = -29.584624385 Simplifying x + 0.5 = -29.584624385 Reorder the terms: 0.5 + x = -29.584624385 Solving 0.5 + x = -29.584624385 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 = -29.584624385 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -29.584624385 + -0.5 x = -29.584624385 + -0.5 Combine like terms: -29.584624385 + -0.5 = -30.084624385 x = -30.084624385 Simplifying x = -30.084624385Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.084624385, -30.084624385}
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