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Simplifying 4x2 + 49x + 49 = 0 Reorder the terms: 49 + 49x + 4x2 = 0 Solving 49 + 49x + 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 + 12.25x + x2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 12.25x + -12.25 + x2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 12.25x + x2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 12.25x + x2 = 0 + -12.25 12.25x + x2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 12.25x + x2 = -12.25 The x term is 12.25x. Take half its coefficient (6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. 12.25x + 37.515625 + x2 = -12.25 + 37.515625 Reorder the terms: 37.515625 + 12.25x + x2 = -12.25 + 37.515625 Combine like terms: -12.25 + 37.515625 = 25.265625 37.515625 + 12.25x + x2 = 25.265625 Factor a perfect square on the left side: (x + 6.125)(x + 6.125) = 25.265625 Calculate the square root of the right side: 5.026492316 Break this problem into two subproblems by setting (x + 6.125) equal to 5.026492316 and -5.026492316.Subproblem 1
x + 6.125 = 5.026492316 Simplifying x + 6.125 = 5.026492316 Reorder the terms: 6.125 + x = 5.026492316 Solving 6.125 + x = 5.026492316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + x = 5.026492316 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = 5.026492316 + -6.125 x = 5.026492316 + -6.125 Combine like terms: 5.026492316 + -6.125 = -1.098507684 x = -1.098507684 Simplifying x = -1.098507684Subproblem 2
x + 6.125 = -5.026492316 Simplifying x + 6.125 = -5.026492316 Reorder the terms: 6.125 + x = -5.026492316 Solving 6.125 + x = -5.026492316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + x = -5.026492316 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = -5.026492316 + -6.125 x = -5.026492316 + -6.125 Combine like terms: -5.026492316 + -6.125 = -11.151492316 x = -11.151492316 Simplifying x = -11.151492316Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.098507684, -11.151492316}
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