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Simplifying 11x2 + -19x + 4 = 0 Reorder the terms: 4 + -19x + 11x2 = 0 Solving 4 + -19x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.3636363636 + -1.727272727x + x2 = 0 Move the constant term to the right: Add '-0.3636363636' to each side of the equation. 0.3636363636 + -1.727272727x + -0.3636363636 + x2 = 0 + -0.3636363636 Reorder the terms: 0.3636363636 + -0.3636363636 + -1.727272727x + x2 = 0 + -0.3636363636 Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000 0.0000000000 + -1.727272727x + x2 = 0 + -0.3636363636 -1.727272727x + x2 = 0 + -0.3636363636 Combine like terms: 0 + -0.3636363636 = -0.3636363636 -1.727272727x + x2 = -0.3636363636 The x term is -1.727272727x. Take half its coefficient (-0.8636363635). Square it (0.7458677684) and add it to both sides. Add '0.7458677684' to each side of the equation. -1.727272727x + 0.7458677684 + x2 = -0.3636363636 + 0.7458677684 Reorder the terms: 0.7458677684 + -1.727272727x + x2 = -0.3636363636 + 0.7458677684 Combine like terms: -0.3636363636 + 0.7458677684 = 0.3822314048 0.7458677684 + -1.727272727x + x2 = 0.3822314048 Factor a perfect square on the left side: (x + -0.8636363635)(x + -0.8636363635) = 0.3822314048 Calculate the square root of the right side: 0.618248659 Break this problem into two subproblems by setting (x + -0.8636363635) equal to 0.618248659 and -0.618248659.Subproblem 1
x + -0.8636363635 = 0.618248659 Simplifying x + -0.8636363635 = 0.618248659 Reorder the terms: -0.8636363635 + x = 0.618248659 Solving -0.8636363635 + x = 0.618248659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8636363635' to each side of the equation. -0.8636363635 + 0.8636363635 + x = 0.618248659 + 0.8636363635 Combine like terms: -0.8636363635 + 0.8636363635 = 0.0000000000 0.0000000000 + x = 0.618248659 + 0.8636363635 x = 0.618248659 + 0.8636363635 Combine like terms: 0.618248659 + 0.8636363635 = 1.4818850225 x = 1.4818850225 Simplifying x = 1.4818850225Subproblem 2
x + -0.8636363635 = -0.618248659 Simplifying x + -0.8636363635 = -0.618248659 Reorder the terms: -0.8636363635 + x = -0.618248659 Solving -0.8636363635 + x = -0.618248659 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8636363635' to each side of the equation. -0.8636363635 + 0.8636363635 + x = -0.618248659 + 0.8636363635 Combine like terms: -0.8636363635 + 0.8636363635 = 0.0000000000 0.0000000000 + x = -0.618248659 + 0.8636363635 x = -0.618248659 + 0.8636363635 Combine like terms: -0.618248659 + 0.8636363635 = 0.2453877045 x = 0.2453877045 Simplifying x = 0.2453877045Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4818850225, 0.2453877045}
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