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Simplifying -8x2 + -6x + 575 = 0 Reorder the terms: 575 + -6x + -8x2 = 0 Solving 575 + -6x + -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'. -71.875 + 0.75x + x2 = 0 Move the constant term to the right: Add '71.875' to each side of the equation. -71.875 + 0.75x + 71.875 + x2 = 0 + 71.875 Reorder the terms: -71.875 + 71.875 + 0.75x + x2 = 0 + 71.875 Combine like terms: -71.875 + 71.875 = 0.000 0.000 + 0.75x + x2 = 0 + 71.875 0.75x + x2 = 0 + 71.875 Combine like terms: 0 + 71.875 = 71.875 0.75x + x2 = 71.875 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 71.875 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 71.875 + 0.140625 Combine like terms: 71.875 + 0.140625 = 72.015625 0.140625 + 0.75x + x2 = 72.015625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 72.015625 Calculate the square root of the right side: 8.486202036 Break this problem into two subproblems by setting (x + 0.375) equal to 8.486202036 and -8.486202036.Subproblem 1
x + 0.375 = 8.486202036 Simplifying x + 0.375 = 8.486202036 Reorder the terms: 0.375 + x = 8.486202036 Solving 0.375 + x = 8.486202036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 8.486202036 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 8.486202036 + -0.375 x = 8.486202036 + -0.375 Combine like terms: 8.486202036 + -0.375 = 8.111202036 x = 8.111202036 Simplifying x = 8.111202036Subproblem 2
x + 0.375 = -8.486202036 Simplifying x + 0.375 = -8.486202036 Reorder the terms: 0.375 + x = -8.486202036 Solving 0.375 + x = -8.486202036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -8.486202036 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -8.486202036 + -0.375 x = -8.486202036 + -0.375 Combine like terms: -8.486202036 + -0.375 = -8.861202036 x = -8.861202036 Simplifying x = -8.861202036Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.111202036, -8.861202036}
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