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Simplifying 2x2 + -1528x + 2821 = 0 Reorder the terms: 2821 + -1528x + 2x2 = 0 Solving 2821 + -1528x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1410.5 + -764x + x2 = 0 Move the constant term to the right: Add '-1410.5' to each side of the equation. 1410.5 + -764x + -1410.5 + x2 = 0 + -1410.5 Reorder the terms: 1410.5 + -1410.5 + -764x + x2 = 0 + -1410.5 Combine like terms: 1410.5 + -1410.5 = 0.0 0.0 + -764x + x2 = 0 + -1410.5 -764x + x2 = 0 + -1410.5 Combine like terms: 0 + -1410.5 = -1410.5 -764x + x2 = -1410.5 The x term is -764x. Take half its coefficient (-382). Square it (145924) and add it to both sides. Add '145924' to each side of the equation. -764x + 145924 + x2 = -1410.5 + 145924 Reorder the terms: 145924 + -764x + x2 = -1410.5 + 145924 Combine like terms: -1410.5 + 145924 = 144513.5 145924 + -764x + x2 = 144513.5 Factor a perfect square on the left side: (x + -382)(x + -382) = 144513.5 Calculate the square root of the right side: 380.149312771 Break this problem into two subproblems by setting (x + -382) equal to 380.149312771 and -380.149312771.Subproblem 1
x + -382 = 380.149312771 Simplifying x + -382 = 380.149312771 Reorder the terms: -382 + x = 380.149312771 Solving -382 + x = 380.149312771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '382' to each side of the equation. -382 + 382 + x = 380.149312771 + 382 Combine like terms: -382 + 382 = 0 0 + x = 380.149312771 + 382 x = 380.149312771 + 382 Combine like terms: 380.149312771 + 382 = 762.149312771 x = 762.149312771 Simplifying x = 762.149312771Subproblem 2
x + -382 = -380.149312771 Simplifying x + -382 = -380.149312771 Reorder the terms: -382 + x = -380.149312771 Solving -382 + x = -380.149312771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '382' to each side of the equation. -382 + 382 + x = -380.149312771 + 382 Combine like terms: -382 + 382 = 0 0 + x = -380.149312771 + 382 x = -380.149312771 + 382 Combine like terms: -380.149312771 + 382 = 1.850687229 x = 1.850687229 Simplifying x = 1.850687229Solution
The solution to the problem is based on the solutions from the subproblems. x = {762.149312771, 1.850687229}
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