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Simplifying 4x2 + -23x + 13 = -7 + 6 Reorder the terms: 13 + -23x + 4x2 = -7 + 6 Combine like terms: -7 + 6 = -1 13 + -23x + 4x2 = -1 Solving 13 + -23x + 4x2 = -1 Solving for variable 'x'. Reorder the terms: 13 + 1 + -23x + 4x2 = -1 + 1 Combine like terms: 13 + 1 = 14 14 + -23x + 4x2 = -1 + 1 Combine like terms: -1 + 1 = 0 14 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -5.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -5.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -5.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -5.75x + x2 = 0 + -3.5 -5.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -5.75x + x2 = -3.5 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 = -3.5 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -3.5 + 8.265625 Combine like terms: -3.5 + 8.265625 = 4.765625 8.265625 + -5.75x + x2 = 4.765625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (x + -2.875) equal to 2.18303115 and -2.18303115.Subproblem 1
x + -2.875 = 2.18303115 Simplifying x + -2.875 = 2.18303115 Reorder the terms: -2.875 + x = 2.18303115 Solving -2.875 + x = 2.18303115 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 = 2.18303115 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 2.18303115 + 2.875 x = 2.18303115 + 2.875 Combine like terms: 2.18303115 + 2.875 = 5.05803115 x = 5.05803115 Simplifying x = 5.05803115Subproblem 2
x + -2.875 = -2.18303115 Simplifying x + -2.875 = -2.18303115 Reorder the terms: -2.875 + x = -2.18303115 Solving -2.875 + x = -2.18303115 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 = -2.18303115 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -2.18303115 + 2.875 x = -2.18303115 + 2.875 Combine like terms: -2.18303115 + 2.875 = 0.69196885 x = 0.69196885 Simplifying x = 0.69196885Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.05803115, 0.69196885}
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