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Simplifying 29x2 + 116x + 16 = 0 Reorder the terms: 16 + 116x + 29x2 = 0 Solving 16 + 116x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. 0.5517241379 + 4x + x2 = 0 Move the constant term to the right: Add '-0.5517241379' to each side of the equation. 0.5517241379 + 4x + -0.5517241379 + x2 = 0 + -0.5517241379 Reorder the terms: 0.5517241379 + -0.5517241379 + 4x + x2 = 0 + -0.5517241379 Combine like terms: 0.5517241379 + -0.5517241379 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + -0.5517241379 4x + x2 = 0 + -0.5517241379 Combine like terms: 0 + -0.5517241379 = -0.5517241379 4x + x2 = -0.5517241379 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -0.5517241379 + 4 Reorder the terms: 4 + 4x + x2 = -0.5517241379 + 4 Combine like terms: -0.5517241379 + 4 = 3.4482758621 4 + 4x + x2 = 3.4482758621 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.4482758621 Calculate the square root of the right side: 1.856953382 Break this problem into two subproblems by setting (x + 2) equal to 1.856953382 and -1.856953382.Subproblem 1
x + 2 = 1.856953382 Simplifying x + 2 = 1.856953382 Reorder the terms: 2 + x = 1.856953382 Solving 2 + x = 1.856953382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.856953382 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.856953382 + -2 x = 1.856953382 + -2 Combine like terms: 1.856953382 + -2 = -0.143046618 x = -0.143046618 Simplifying x = -0.143046618Subproblem 2
x + 2 = -1.856953382 Simplifying x + 2 = -1.856953382 Reorder the terms: 2 + x = -1.856953382 Solving 2 + x = -1.856953382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.856953382 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.856953382 + -2 x = -1.856953382 + -2 Combine like terms: -1.856953382 + -2 = -3.856953382 x = -3.856953382 Simplifying x = -3.856953382Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.143046618, -3.856953382}
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