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Simplifying -8x2 + 250x + 3 = 0 Reorder the terms: 3 + 250x + -8x2 = 0 Solving 3 + 250x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -31.25x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -31.25x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -31.25x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -31.25x + x2 = 0 + 0.375 -31.25x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -31.25x + x2 = 0.375 The x term is -31.25x. Take half its coefficient (-15.625). Square it (244.140625) and add it to both sides. Add '244.140625' to each side of the equation. -31.25x + 244.140625 + x2 = 0.375 + 244.140625 Reorder the terms: 244.140625 + -31.25x + x2 = 0.375 + 244.140625 Combine like terms: 0.375 + 244.140625 = 244.515625 244.140625 + -31.25x + x2 = 244.515625 Factor a perfect square on the left side: (x + -15.625)(x + -15.625) = 244.515625 Calculate the square root of the right side: 15.636995396 Break this problem into two subproblems by setting (x + -15.625) equal to 15.636995396 and -15.636995396.Subproblem 1
x + -15.625 = 15.636995396 Simplifying x + -15.625 = 15.636995396 Reorder the terms: -15.625 + x = 15.636995396 Solving -15.625 + x = 15.636995396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = 15.636995396 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = 15.636995396 + 15.625 x = 15.636995396 + 15.625 Combine like terms: 15.636995396 + 15.625 = 31.261995396 x = 31.261995396 Simplifying x = 31.261995396Subproblem 2
x + -15.625 = -15.636995396 Simplifying x + -15.625 = -15.636995396 Reorder the terms: -15.625 + x = -15.636995396 Solving -15.625 + x = -15.636995396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.625' to each side of the equation. -15.625 + 15.625 + x = -15.636995396 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + x = -15.636995396 + 15.625 x = -15.636995396 + 15.625 Combine like terms: -15.636995396 + 15.625 = -0.011995396 x = -0.011995396 Simplifying x = -0.011995396Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.261995396, -0.011995396}
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