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Simplifying 2x2 + -1x + -2352 = 0 Reorder the terms: -2352 + -1x + 2x2 = 0 Solving -2352 + -1x + 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'. -1176 + -0.5x + x2 = 0 Move the constant term to the right: Add '1176' to each side of the equation. -1176 + -0.5x + 1176 + x2 = 0 + 1176 Reorder the terms: -1176 + 1176 + -0.5x + x2 = 0 + 1176 Combine like terms: -1176 + 1176 = 0 0 + -0.5x + x2 = 0 + 1176 -0.5x + x2 = 0 + 1176 Combine like terms: 0 + 1176 = 1176 -0.5x + x2 = 1176 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1176 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1176 + 0.0625 Combine like terms: 1176 + 0.0625 = 1176.0625 0.0625 + -0.5x + x2 = 1176.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1176.0625 Calculate the square root of the right side: 34.293767655 Break this problem into two subproblems by setting (x + -0.25) equal to 34.293767655 and -34.293767655.Subproblem 1
x + -0.25 = 34.293767655 Simplifying x + -0.25 = 34.293767655 Reorder the terms: -0.25 + x = 34.293767655 Solving -0.25 + x = 34.293767655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 34.293767655 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 34.293767655 + 0.25 x = 34.293767655 + 0.25 Combine like terms: 34.293767655 + 0.25 = 34.543767655 x = 34.543767655 Simplifying x = 34.543767655Subproblem 2
x + -0.25 = -34.293767655 Simplifying x + -0.25 = -34.293767655 Reorder the terms: -0.25 + x = -34.293767655 Solving -0.25 + x = -34.293767655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -34.293767655 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -34.293767655 + 0.25 x = -34.293767655 + 0.25 Combine like terms: -34.293767655 + 0.25 = -34.043767655 x = -34.043767655 Simplifying x = -34.043767655Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.543767655, -34.043767655}
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