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Simplifying 4x2 + 23x + 1 = 0 Reorder the terms: 1 + 23x + 4x2 = 0 Solving 1 + 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'. 0.25 + 5.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 5.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 5.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 5.75x + x2 = 0 + -0.25 5.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 5.75x + x2 = -0.25 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 = -0.25 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = -0.25 + 8.265625 Combine like terms: -0.25 + 8.265625 = 8.015625 8.265625 + 5.75x + x2 = 8.015625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 8.015625 Calculate the square root of the right side: 2.831187913 Break this problem into two subproblems by setting (x + 2.875) equal to 2.831187913 and -2.831187913.Subproblem 1
x + 2.875 = 2.831187913 Simplifying x + 2.875 = 2.831187913 Reorder the terms: 2.875 + x = 2.831187913 Solving 2.875 + x = 2.831187913 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 = 2.831187913 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 2.831187913 + -2.875 x = 2.831187913 + -2.875 Combine like terms: 2.831187913 + -2.875 = -0.043812087 x = -0.043812087 Simplifying x = -0.043812087Subproblem 2
x + 2.875 = -2.831187913 Simplifying x + 2.875 = -2.831187913 Reorder the terms: 2.875 + x = -2.831187913 Solving 2.875 + x = -2.831187913 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 = -2.831187913 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -2.831187913 + -2.875 x = -2.831187913 + -2.875 Combine like terms: -2.831187913 + -2.875 = -5.706187913 x = -5.706187913 Simplifying x = -5.706187913Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.043812087, -5.706187913}
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