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Simplifying 8x2 = 1 + -6x Solving 8x2 = 1 + -6x Solving for variable 'x'. Reorder the terms: -1 + 6x + 8x2 = 1 + -6x + -1 + 6x Reorder the terms: -1 + 6x + 8x2 = 1 + -1 + -6x + 6x Combine like terms: 1 + -1 = 0 -1 + 6x + 8x2 = 0 + -6x + 6x -1 + 6x + 8x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -1 + 6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 0.75x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 0.75x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 0.75x + x2 = 0 + 0.125 0.75x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 0.75x + x2 = 0.125 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 = 0.125 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.125 + 0.140625 Combine like terms: 0.125 + 0.140625 = 0.265625 0.140625 + 0.75x + x2 = 0.265625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + 0.375) equal to 0.515388203 and -0.515388203.Subproblem 1
x + 0.375 = 0.515388203 Simplifying x + 0.375 = 0.515388203 Reorder the terms: 0.375 + x = 0.515388203 Solving 0.375 + x = 0.515388203 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 = 0.515388203 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.515388203 + -0.375 x = 0.515388203 + -0.375 Combine like terms: 0.515388203 + -0.375 = 0.140388203 x = 0.140388203 Simplifying x = 0.140388203Subproblem 2
x + 0.375 = -0.515388203 Simplifying x + 0.375 = -0.515388203 Reorder the terms: 0.375 + x = -0.515388203 Solving 0.375 + x = -0.515388203 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 = -0.515388203 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.515388203 + -0.375 x = -0.515388203 + -0.375 Combine like terms: -0.515388203 + -0.375 = -0.890388203 x = -0.890388203 Simplifying x = -0.890388203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.140388203, -0.890388203}
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