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Simplifying 16x2 + 56x + -49 = 0 Reorder the terms: -49 + 56x + 16x2 = 0 Solving -49 + 56x + 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'. -3.0625 + 3.5x + x2 = 0 Move the constant term to the right: Add '3.0625' to each side of the equation. -3.0625 + 3.5x + 3.0625 + x2 = 0 + 3.0625 Reorder the terms: -3.0625 + 3.0625 + 3.5x + x2 = 0 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + 3.5x + x2 = 0 + 3.0625 3.5x + x2 = 0 + 3.0625 Combine like terms: 0 + 3.0625 = 3.0625 3.5x + x2 = 3.0625 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 3.0625 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 3.0625 + 3.0625 Combine like terms: 3.0625 + 3.0625 = 6.125 3.0625 + 3.5x + x2 = 6.125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 6.125 Calculate the square root of the right side: 2.474873734 Break this problem into two subproblems by setting (x + 1.75) equal to 2.474873734 and -2.474873734.Subproblem 1
x + 1.75 = 2.474873734 Simplifying x + 1.75 = 2.474873734 Reorder the terms: 1.75 + x = 2.474873734 Solving 1.75 + x = 2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 2.474873734 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 2.474873734 + -1.75 x = 2.474873734 + -1.75 Combine like terms: 2.474873734 + -1.75 = 0.724873734 x = 0.724873734 Simplifying x = 0.724873734Subproblem 2
x + 1.75 = -2.474873734 Simplifying x + 1.75 = -2.474873734 Reorder the terms: 1.75 + x = -2.474873734 Solving 1.75 + x = -2.474873734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -2.474873734 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -2.474873734 + -1.75 x = -2.474873734 + -1.75 Combine like terms: -2.474873734 + -1.75 = -4.224873734 x = -4.224873734 Simplifying x = -4.224873734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.724873734, -4.224873734}
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