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Simplifying 19x2 + -1984x + 5120 = 0 Reorder the terms: 5120 + -1984x + 19x2 = 0 Solving 5120 + -1984x + 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'. 269.4736842 + -104.4210526x + x2 = 0 Move the constant term to the right: Add '-269.4736842' to each side of the equation. 269.4736842 + -104.4210526x + -269.4736842 + x2 = 0 + -269.4736842 Reorder the terms: 269.4736842 + -269.4736842 + -104.4210526x + x2 = 0 + -269.4736842 Combine like terms: 269.4736842 + -269.4736842 = 0.0000000 0.0000000 + -104.4210526x + x2 = 0 + -269.4736842 -104.4210526x + x2 = 0 + -269.4736842 Combine like terms: 0 + -269.4736842 = -269.4736842 -104.4210526x + x2 = -269.4736842 The x term is -104.4210526x. Take half its coefficient (-52.2105263). Square it (2725.939057) and add it to both sides. Add '2725.939057' to each side of the equation. -104.4210526x + 2725.939057 + x2 = -269.4736842 + 2725.939057 Reorder the terms: 2725.939057 + -104.4210526x + x2 = -269.4736842 + 2725.939057 Combine like terms: -269.4736842 + 2725.939057 = 2456.4653728 2725.939057 + -104.4210526x + x2 = 2456.4653728 Factor a perfect square on the left side: (x + -52.2105263)(x + -52.2105263) = 2456.4653728 Calculate the square root of the right side: 49.56274178 Break this problem into two subproblems by setting (x + -52.2105263) equal to 49.56274178 and -49.56274178.Subproblem 1
x + -52.2105263 = 49.56274178 Simplifying x + -52.2105263 = 49.56274178 Reorder the terms: -52.2105263 + x = 49.56274178 Solving -52.2105263 + x = 49.56274178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.2105263' to each side of the equation. -52.2105263 + 52.2105263 + x = 49.56274178 + 52.2105263 Combine like terms: -52.2105263 + 52.2105263 = 0.0000000 0.0000000 + x = 49.56274178 + 52.2105263 x = 49.56274178 + 52.2105263 Combine like terms: 49.56274178 + 52.2105263 = 101.77326808 x = 101.77326808 Simplifying x = 101.77326808Subproblem 2
x + -52.2105263 = -49.56274178 Simplifying x + -52.2105263 = -49.56274178 Reorder the terms: -52.2105263 + x = -49.56274178 Solving -52.2105263 + x = -49.56274178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52.2105263' to each side of the equation. -52.2105263 + 52.2105263 + x = -49.56274178 + 52.2105263 Combine like terms: -52.2105263 + 52.2105263 = 0.0000000 0.0000000 + x = -49.56274178 + 52.2105263 x = -49.56274178 + 52.2105263 Combine like terms: -49.56274178 + 52.2105263 = 2.64778452 x = 2.64778452 Simplifying x = 2.64778452Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.77326808, 2.64778452}
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