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Simplifying 2x2 + -57x + -8000 = 0 Reorder the terms: -8000 + -57x + 2x2 = 0 Solving -8000 + -57x + 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'. -4000 + -28.5x + x2 = 0 Move the constant term to the right: Add '4000' to each side of the equation. -4000 + -28.5x + 4000 + x2 = 0 + 4000 Reorder the terms: -4000 + 4000 + -28.5x + x2 = 0 + 4000 Combine like terms: -4000 + 4000 = 0 0 + -28.5x + x2 = 0 + 4000 -28.5x + x2 = 0 + 4000 Combine like terms: 0 + 4000 = 4000 -28.5x + x2 = 4000 The x term is -28.5x. Take half its coefficient (-14.25). Square it (203.0625) and add it to both sides. Add '203.0625' to each side of the equation. -28.5x + 203.0625 + x2 = 4000 + 203.0625 Reorder the terms: 203.0625 + -28.5x + x2 = 4000 + 203.0625 Combine like terms: 4000 + 203.0625 = 4203.0625 203.0625 + -28.5x + x2 = 4203.0625 Factor a perfect square on the left side: (x + -14.25)(x + -14.25) = 4203.0625 Calculate the square root of the right side: 64.831030379 Break this problem into two subproblems by setting (x + -14.25) equal to 64.831030379 and -64.831030379.Subproblem 1
x + -14.25 = 64.831030379 Simplifying x + -14.25 = 64.831030379 Reorder the terms: -14.25 + x = 64.831030379 Solving -14.25 + x = 64.831030379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.25' to each side of the equation. -14.25 + 14.25 + x = 64.831030379 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + x = 64.831030379 + 14.25 x = 64.831030379 + 14.25 Combine like terms: 64.831030379 + 14.25 = 79.081030379 x = 79.081030379 Simplifying x = 79.081030379Subproblem 2
x + -14.25 = -64.831030379 Simplifying x + -14.25 = -64.831030379 Reorder the terms: -14.25 + x = -64.831030379 Solving -14.25 + x = -64.831030379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.25' to each side of the equation. -14.25 + 14.25 + x = -64.831030379 + 14.25 Combine like terms: -14.25 + 14.25 = 0.00 0.00 + x = -64.831030379 + 14.25 x = -64.831030379 + 14.25 Combine like terms: -64.831030379 + 14.25 = -50.581030379 x = -50.581030379 Simplifying x = -50.581030379Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.081030379, -50.581030379}
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