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Simplifying 8x2 + 111x + 3 = 0 Reorder the terms: 3 + 111x + 8x2 = 0 Solving 3 + 111x + 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 + 13.875x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 13.875x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 13.875x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 13.875x + x2 = 0 + -0.375 13.875x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 13.875x + x2 = -0.375 The x term is 13.875x. Take half its coefficient (6.9375). Square it (48.12890625) and add it to both sides. Add '48.12890625' to each side of the equation. 13.875x + 48.12890625 + x2 = -0.375 + 48.12890625 Reorder the terms: 48.12890625 + 13.875x + x2 = -0.375 + 48.12890625 Combine like terms: -0.375 + 48.12890625 = 47.75390625 48.12890625 + 13.875x + x2 = 47.75390625 Factor a perfect square on the left side: (x + 6.9375)(x + 6.9375) = 47.75390625 Calculate the square root of the right side: 6.910420121 Break this problem into two subproblems by setting (x + 6.9375) equal to 6.910420121 and -6.910420121.Subproblem 1
x + 6.9375 = 6.910420121 Simplifying x + 6.9375 = 6.910420121 Reorder the terms: 6.9375 + x = 6.910420121 Solving 6.9375 + x = 6.910420121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.9375' to each side of the equation. 6.9375 + -6.9375 + x = 6.910420121 + -6.9375 Combine like terms: 6.9375 + -6.9375 = 0.0000 0.0000 + x = 6.910420121 + -6.9375 x = 6.910420121 + -6.9375 Combine like terms: 6.910420121 + -6.9375 = -0.027079879 x = -0.027079879 Simplifying x = -0.027079879Subproblem 2
x + 6.9375 = -6.910420121 Simplifying x + 6.9375 = -6.910420121 Reorder the terms: 6.9375 + x = -6.910420121 Solving 6.9375 + x = -6.910420121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.9375' to each side of the equation. 6.9375 + -6.9375 + x = -6.910420121 + -6.9375 Combine like terms: 6.9375 + -6.9375 = 0.0000 0.0000 + x = -6.910420121 + -6.9375 x = -6.910420121 + -6.9375 Combine like terms: -6.910420121 + -6.9375 = -13.847920121 x = -13.847920121 Simplifying x = -13.847920121Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.027079879, -13.847920121}
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