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Simplifying 4x2 + 23x + 3 = 0 Reorder the terms: 3 + 23x + 4x2 = 0 Solving 3 + 23x + 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'. 0.75 + 5.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 5.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 5.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 5.75x + x2 = 0 + -0.75 5.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 5.75x + x2 = -0.75 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = -0.75 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -0.75 + 8.265625 Combine like terms: -0.75 + 8.265625 = 7.515625 8.265625 + 5.75x + x2 = 7.515625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + 2.875) equal to 2.741464025 and -2.741464025.Subproblem 1
x + 2.875 = 2.741464025 Simplifying x + 2.875 = 2.741464025 Reorder the terms: 2.875 + x = 2.741464025 Solving 2.875 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 2.741464025 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 2.741464025 + -2.875 x = 2.741464025 + -2.875 Combine like terms: 2.741464025 + -2.875 = -0.133535975 x = -0.133535975 Simplifying x = -0.133535975Subproblem 2
x + 2.875 = -2.741464025 Simplifying x + 2.875 = -2.741464025 Reorder the terms: 2.875 + x = -2.741464025 Solving 2.875 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -2.741464025 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -2.741464025 + -2.875 x = -2.741464025 + -2.875 Combine like terms: -2.741464025 + -2.875 = -5.616464025 x = -5.616464025 Simplifying x = -5.616464025Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.133535975, -5.616464025}
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