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Simplifying 4x2 + 23x + -2 = 0 Reorder the terms: -2 + 23x + 4x2 = 0 Solving -2 + 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'. -0.5 + 5.75x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 5.75x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 5.75x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 5.75x + x2 = 0 + 0.5 5.75x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 5.75x + x2 = 0.5 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 = 0.5 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 0.5 + 8.265625 Combine like terms: 0.5 + 8.265625 = 8.765625 8.265625 + 5.75x + x2 = 8.765625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 8.765625 Calculate the square root of the right side: 2.960679821 Break this problem into two subproblems by setting (x + 2.875) equal to 2.960679821 and -2.960679821.Subproblem 1
x + 2.875 = 2.960679821 Simplifying x + 2.875 = 2.960679821 Reorder the terms: 2.875 + x = 2.960679821 Solving 2.875 + x = 2.960679821 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 = 2.960679821 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 2.960679821 + -2.875 x = 2.960679821 + -2.875 Combine like terms: 2.960679821 + -2.875 = 0.085679821 x = 0.085679821 Simplifying x = 0.085679821Subproblem 2
x + 2.875 = -2.960679821 Simplifying x + 2.875 = -2.960679821 Reorder the terms: 2.875 + x = -2.960679821 Solving 2.875 + x = -2.960679821 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 = -2.960679821 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -2.960679821 + -2.875 x = -2.960679821 + -2.875 Combine like terms: -2.960679821 + -2.875 = -5.835679821 x = -5.835679821 Simplifying x = -5.835679821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.085679821, -5.835679821}
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