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Simplifying 4x2 + 0.33x + -0.33 = 0 Reorder the terms: -0.33 + 0.33x + 4x2 = 0 Solving -0.33 + 0.33x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.0825 + 0.0825x + x2 = 0 Move the constant term to the right: Add '0.0825' to each side of the equation. -0.0825 + 0.0825x + 0.0825 + x2 = 0 + 0.0825 Reorder the terms: -0.0825 + 0.0825 + 0.0825x + x2 = 0 + 0.0825 Combine like terms: -0.0825 + 0.0825 = 0.0000 0.0000 + 0.0825x + x2 = 0 + 0.0825 0.0825x + x2 = 0 + 0.0825 Combine like terms: 0 + 0.0825 = 0.0825 0.0825x + x2 = 0.0825 The x term is 0.0825x. Take half its coefficient (0.04125). Square it (0.0017015625) and add it to both sides. Add '0.0017015625' to each side of the equation. 0.0825x + 0.0017015625 + x2 = 0.0825 + 0.0017015625 Reorder the terms: 0.0017015625 + 0.0825x + x2 = 0.0825 + 0.0017015625 Combine like terms: 0.0825 + 0.0017015625 = 0.0842015625 0.0017015625 + 0.0825x + x2 = 0.0842015625 Factor a perfect square on the left side: (x + 0.04125)(x + 0.04125) = 0.0842015625 Calculate the square root of the right side: 0.290175055 Break this problem into two subproblems by setting (x + 0.04125) equal to 0.290175055 and -0.290175055.Subproblem 1
x + 0.04125 = 0.290175055 Simplifying x + 0.04125 = 0.290175055 Reorder the terms: 0.04125 + x = 0.290175055 Solving 0.04125 + x = 0.290175055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + x = 0.290175055 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + x = 0.290175055 + -0.04125 x = 0.290175055 + -0.04125 Combine like terms: 0.290175055 + -0.04125 = 0.248925055 x = 0.248925055 Simplifying x = 0.248925055Subproblem 2
x + 0.04125 = -0.290175055 Simplifying x + 0.04125 = -0.290175055 Reorder the terms: 0.04125 + x = -0.290175055 Solving 0.04125 + x = -0.290175055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + x = -0.290175055 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + x = -0.290175055 + -0.04125 x = -0.290175055 + -0.04125 Combine like terms: -0.290175055 + -0.04125 = -0.331425055 x = -0.331425055 Simplifying x = -0.331425055Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.248925055, -0.331425055}
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