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Simplifying 19x2 + -2000x + 6000 = 0 Reorder the terms: 6000 + -2000x + 19x2 = 0 Solving 6000 + -2000x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 315.7894737 + -105.2631579x + x2 = 0 Move the constant term to the right: Add '-315.7894737' to each side of the equation. 315.7894737 + -105.2631579x + -315.7894737 + x2 = 0 + -315.7894737 Reorder the terms: 315.7894737 + -315.7894737 + -105.2631579x + x2 = 0 + -315.7894737 Combine like terms: 315.7894737 + -315.7894737 = 0.0000000 0.0000000 + -105.2631579x + x2 = 0 + -315.7894737 -105.2631579x + x2 = 0 + -315.7894737 Combine like terms: 0 + -315.7894737 = -315.7894737 -105.2631579x + x2 = -315.7894737 The x term is -105.2631579x. Take half its coefficient (-52.63157895). Square it (2770.083103) and add it to both sides. Add '2770.083103' to each side of the equation. -105.2631579x + 2770.083103 + x2 = -315.7894737 + 2770.083103 Reorder the terms: 2770.083103 + -105.2631579x + x2 = -315.7894737 + 2770.083103 Combine like terms: -315.7894737 + 2770.083103 = 2454.2936293 2770.083103 + -105.2631579x + x2 = 2454.2936293 Factor a perfect square on the left side: (x + -52.63157895)(x + -52.63157895) = 2454.2936293 Calculate the square root of the right side: 49.540827903 Break this problem into two subproblems by setting (x + -52.63157895) equal to 49.540827903 and -49.540827903.Subproblem 1
x + -52.63157895 = 49.540827903 Simplifying x + -52.63157895 = 49.540827903 Reorder the terms: -52.63157895 + x = 49.540827903 Solving -52.63157895 + x = 49.540827903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.63157895' to each side of the equation. -52.63157895 + 52.63157895 + x = 49.540827903 + 52.63157895 Combine like terms: -52.63157895 + 52.63157895 = 0.00000000 0.00000000 + x = 49.540827903 + 52.63157895 x = 49.540827903 + 52.63157895 Combine like terms: 49.540827903 + 52.63157895 = 102.172406853 x = 102.172406853 Simplifying x = 102.172406853Subproblem 2
x + -52.63157895 = -49.540827903 Simplifying x + -52.63157895 = -49.540827903 Reorder the terms: -52.63157895 + x = -49.540827903 Solving -52.63157895 + x = -49.540827903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.63157895' to each side of the equation. -52.63157895 + 52.63157895 + x = -49.540827903 + 52.63157895 Combine like terms: -52.63157895 + 52.63157895 = 0.00000000 0.00000000 + x = -49.540827903 + 52.63157895 x = -49.540827903 + 52.63157895 Combine like terms: -49.540827903 + 52.63157895 = 3.090751047 x = 3.090751047 Simplifying x = 3.090751047Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.172406853, 3.090751047}
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