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Simplifying 4x2 + -38x + 49 = 0 Reorder the terms: 49 + -38x + 4x2 = 0 Solving 49 + -38x + 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 + -9.5x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + -9.5x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + -9.5x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + -9.5x + x2 = 0 + -12.25 -9.5x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 -9.5x + x2 = -12.25 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = -12.25 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = -12.25 + 22.5625 Combine like terms: -12.25 + 22.5625 = 10.3125 22.5625 + -9.5x + x2 = 10.3125 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 10.3125 Calculate the square root of the right side: 3.211308145 Break this problem into two subproblems by setting (x + -4.75) equal to 3.211308145 and -3.211308145.Subproblem 1
x + -4.75 = 3.211308145 Simplifying x + -4.75 = 3.211308145 Reorder the terms: -4.75 + x = 3.211308145 Solving -4.75 + x = 3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 3.211308145 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 3.211308145 + 4.75 x = 3.211308145 + 4.75 Combine like terms: 3.211308145 + 4.75 = 7.961308145 x = 7.961308145 Simplifying x = 7.961308145Subproblem 2
x + -4.75 = -3.211308145 Simplifying x + -4.75 = -3.211308145 Reorder the terms: -4.75 + x = -3.211308145 Solving -4.75 + x = -3.211308145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -3.211308145 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -3.211308145 + 4.75 x = -3.211308145 + 4.75 Combine like terms: -3.211308145 + 4.75 = 1.538691855 x = 1.538691855 Simplifying x = 1.538691855Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.961308145, 1.538691855}
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