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Simplifying 16x2 + 41x + 14 = 0 Reorder the terms: 14 + 41x + 16x2 = 0 Solving 14 + 41x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.875 + 2.5625x + x2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 2.5625x + -0.875 + x2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 2.5625x + x2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 2.5625x + x2 = 0 + -0.875 2.5625x + x2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 2.5625x + x2 = -0.875 The x term is 2.5625x. Take half its coefficient (1.28125). Square it (1.641601563) and add it to both sides. Add '1.641601563' to each side of the equation. 2.5625x + 1.641601563 + x2 = -0.875 + 1.641601563 Reorder the terms: 1.641601563 + 2.5625x + x2 = -0.875 + 1.641601563 Combine like terms: -0.875 + 1.641601563 = 0.766601563 1.641601563 + 2.5625x + x2 = 0.766601563 Factor a perfect square on the left side: (x + 1.28125)(x + 1.28125) = 0.766601563 Calculate the square root of the right side: 0.875557858 Break this problem into two subproblems by setting (x + 1.28125) equal to 0.875557858 and -0.875557858.Subproblem 1
x + 1.28125 = 0.875557858 Simplifying x + 1.28125 = 0.875557858 Reorder the terms: 1.28125 + x = 0.875557858 Solving 1.28125 + x = 0.875557858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.28125' to each side of the equation. 1.28125 + -1.28125 + x = 0.875557858 + -1.28125 Combine like terms: 1.28125 + -1.28125 = 0.00000 0.00000 + x = 0.875557858 + -1.28125 x = 0.875557858 + -1.28125 Combine like terms: 0.875557858 + -1.28125 = -0.405692142 x = -0.405692142 Simplifying x = -0.405692142Subproblem 2
x + 1.28125 = -0.875557858 Simplifying x + 1.28125 = -0.875557858 Reorder the terms: 1.28125 + x = -0.875557858 Solving 1.28125 + x = -0.875557858 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.28125' to each side of the equation. 1.28125 + -1.28125 + x = -0.875557858 + -1.28125 Combine like terms: 1.28125 + -1.28125 = 0.00000 0.00000 + x = -0.875557858 + -1.28125 x = -0.875557858 + -1.28125 Combine like terms: -0.875557858 + -1.28125 = -2.156807858 x = -2.156807858 Simplifying x = -2.156807858Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.405692142, -2.156807858}
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