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Simplifying 2 = -32x2 + 8x + 3 Reorder the terms: 2 = 3 + 8x + -32x2 Solving 2 = 3 + 8x + -32x2 Solving for variable 'x'. Combine like terms: 2 + -3 = -1 -1 + -8x + 32x2 = 3 + 8x + -32x2 + -3 + -8x + 32x2 Reorder the terms: -1 + -8x + 32x2 = 3 + -3 + 8x + -8x + -32x2 + 32x2 Combine like terms: 3 + -3 = 0 -1 + -8x + 32x2 = 0 + 8x + -8x + -32x2 + 32x2 -1 + -8x + 32x2 = 8x + -8x + -32x2 + 32x2 Combine like terms: 8x + -8x = 0 -1 + -8x + 32x2 = 0 + -32x2 + 32x2 -1 + -8x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -1 + -8x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.03125 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + -0.25x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + -0.25x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + -0.25x + x2 = 0 + 0.03125 -0.25x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 -0.25x + x2 = 0.03125 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.03125 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.03125 + 0.015625 Combine like terms: 0.03125 + 0.015625 = 0.046875 0.015625 + -0.25x + x2 = 0.046875 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.046875 Calculate the square root of the right side: 0.216506351 Break this problem into two subproblems by setting (x + -0.125) equal to 0.216506351 and -0.216506351.Subproblem 1
x + -0.125 = 0.216506351 Simplifying x + -0.125 = 0.216506351 Reorder the terms: -0.125 + x = 0.216506351 Solving -0.125 + x = 0.216506351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.216506351 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.216506351 + 0.125 x = 0.216506351 + 0.125 Combine like terms: 0.216506351 + 0.125 = 0.341506351 x = 0.341506351 Simplifying x = 0.341506351Subproblem 2
x + -0.125 = -0.216506351 Simplifying x + -0.125 = -0.216506351 Reorder the terms: -0.125 + x = -0.216506351 Solving -0.125 + x = -0.216506351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.216506351 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.216506351 + 0.125 x = -0.216506351 + 0.125 Combine like terms: -0.216506351 + 0.125 = -0.091506351 x = -0.091506351 Simplifying x = -0.091506351Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.341506351, -0.091506351}
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