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Simplifying 4x2 + 118x + 49 = 0 Reorder the terms: 49 + 118x + 4x2 = 0 Solving 49 + 118x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + 29.5x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 29.5x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 29.5x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 29.5x + x2 = 0 + -12.25 29.5x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 29.5x + x2 = -12.25 The x term is 29.5x. Take half its coefficient (14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. 29.5x + 217.5625 + x2 = -12.25 + 217.5625 Reorder the terms: 217.5625 + 29.5x + x2 = -12.25 + 217.5625 Combine like terms: -12.25 + 217.5625 = 205.3125 217.5625 + 29.5x + x2 = 205.3125 Factor a perfect square on the left side: (x + 14.75)(x + 14.75) = 205.3125 Calculate the square root of the right side: 14.328729881 Break this problem into two subproblems by setting (x + 14.75) equal to 14.328729881 and -14.328729881.Subproblem 1
x + 14.75 = 14.328729881 Simplifying x + 14.75 = 14.328729881 Reorder the terms: 14.75 + x = 14.328729881 Solving 14.75 + x = 14.328729881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.75' to each side of the equation. 14.75 + -14.75 + x = 14.328729881 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + x = 14.328729881 + -14.75 x = 14.328729881 + -14.75 Combine like terms: 14.328729881 + -14.75 = -0.421270119 x = -0.421270119 Simplifying x = -0.421270119Subproblem 2
x + 14.75 = -14.328729881 Simplifying x + 14.75 = -14.328729881 Reorder the terms: 14.75 + x = -14.328729881 Solving 14.75 + x = -14.328729881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.75' to each side of the equation. 14.75 + -14.75 + x = -14.328729881 + -14.75 Combine like terms: 14.75 + -14.75 = 0.00 0.00 + x = -14.328729881 + -14.75 x = -14.328729881 + -14.75 Combine like terms: -14.328729881 + -14.75 = -29.078729881 x = -29.078729881 Simplifying x = -29.078729881Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.421270119, -29.078729881}
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