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Simplifying 196x2 + 49x + 2 = 0 Reorder the terms: 2 + 49x + 196x2 = 0 Solving 2 + 49x + 196x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 196 the coefficient of the squared term: Divide each side by '196'. 0.01020408163 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.01020408163' to each side of the equation. 0.01020408163 + 0.25x + -0.01020408163 + x2 = 0 + -0.01020408163 Reorder the terms: 0.01020408163 + -0.01020408163 + 0.25x + x2 = 0 + -0.01020408163 Combine like terms: 0.01020408163 + -0.01020408163 = 0.00000000000 0.00000000000 + 0.25x + x2 = 0 + -0.01020408163 0.25x + x2 = 0 + -0.01020408163 Combine like terms: 0 + -0.01020408163 = -0.01020408163 0.25x + x2 = -0.01020408163 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = -0.01020408163 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -0.01020408163 + 0.015625 Combine like terms: -0.01020408163 + 0.015625 = 0.00542091837 0.015625 + 0.25x + x2 = 0.00542091837 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.00542091837 Calculate the square root of the right side: 0.073626886 Break this problem into two subproblems by setting (x + 0.125) equal to 0.073626886 and -0.073626886.Subproblem 1
x + 0.125 = 0.073626886 Simplifying x + 0.125 = 0.073626886 Reorder the terms: 0.125 + x = 0.073626886 Solving 0.125 + x = 0.073626886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.073626886 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.073626886 + -0.125 x = 0.073626886 + -0.125 Combine like terms: 0.073626886 + -0.125 = -0.051373114 x = -0.051373114 Simplifying x = -0.051373114Subproblem 2
x + 0.125 = -0.073626886 Simplifying x + 0.125 = -0.073626886 Reorder the terms: 0.125 + x = -0.073626886 Solving 0.125 + x = -0.073626886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.073626886 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.073626886 + -0.125 x = -0.073626886 + -0.125 Combine like terms: -0.073626886 + -0.125 = -0.198626886 x = -0.198626886 Simplifying x = -0.198626886Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.051373114, -0.198626886}
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