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Simplifying 12x2 + -49x + 48 = 0 Reorder the terms: 48 + -49x + 12x2 = 0 Solving 48 + -49x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 4 + -4.083333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.083333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -4.083333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.083333333x + x2 = 0 + -4 -4.083333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.083333333x + x2 = -4 The x term is -4.083333333x. Take half its coefficient (-2.041666667). Square it (4.168402779) and add it to both sides. Add '4.168402779' to each side of the equation. -4.083333333x + 4.168402779 + x2 = -4 + 4.168402779 Reorder the terms: 4.168402779 + -4.083333333x + x2 = -4 + 4.168402779 Combine like terms: -4 + 4.168402779 = 0.168402779 4.168402779 + -4.083333333x + x2 = 0.168402779 Factor a perfect square on the left side: (x + -2.041666667)(x + -2.041666667) = 0.168402779 Calculate the square root of the right side: 0.410369077 Break this problem into two subproblems by setting (x + -2.041666667) equal to 0.410369077 and -0.410369077.Subproblem 1
x + -2.041666667 = 0.410369077 Simplifying x + -2.041666667 = 0.410369077 Reorder the terms: -2.041666667 + x = 0.410369077 Solving -2.041666667 + x = 0.410369077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + x = 0.410369077 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + x = 0.410369077 + 2.041666667 x = 0.410369077 + 2.041666667 Combine like terms: 0.410369077 + 2.041666667 = 2.452035744 x = 2.452035744 Simplifying x = 2.452035744Subproblem 2
x + -2.041666667 = -0.410369077 Simplifying x + -2.041666667 = -0.410369077 Reorder the terms: -2.041666667 + x = -0.410369077 Solving -2.041666667 + x = -0.410369077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.041666667' to each side of the equation. -2.041666667 + 2.041666667 + x = -0.410369077 + 2.041666667 Combine like terms: -2.041666667 + 2.041666667 = 0.000000000 0.000000000 + x = -0.410369077 + 2.041666667 x = -0.410369077 + 2.041666667 Combine like terms: -0.410369077 + 2.041666667 = 1.63129759 x = 1.63129759 Simplifying x = 1.63129759Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.452035744, 1.63129759}
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