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Simplifying 2x2 + 25x + -2000 = 0 Reorder the terms: -2000 + 25x + 2x2 = 0 Solving -2000 + 25x + 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'. -1000 + 12.5x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 12.5x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 12.5x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 12.5x + x2 = 0 + 1000 12.5x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 12.5x + x2 = 1000 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 1000 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 1000 + 39.0625 Combine like terms: 1000 + 39.0625 = 1039.0625 39.0625 + 12.5x + x2 = 1039.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 1039.0625 Calculate the square root of the right side: 32.234492396 Break this problem into two subproblems by setting (x + 6.25) equal to 32.234492396 and -32.234492396.Subproblem 1
x + 6.25 = 32.234492396 Simplifying x + 6.25 = 32.234492396 Reorder the terms: 6.25 + x = 32.234492396 Solving 6.25 + x = 32.234492396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 32.234492396 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 32.234492396 + -6.25 x = 32.234492396 + -6.25 Combine like terms: 32.234492396 + -6.25 = 25.984492396 x = 25.984492396 Simplifying x = 25.984492396Subproblem 2
x + 6.25 = -32.234492396 Simplifying x + 6.25 = -32.234492396 Reorder the terms: 6.25 + x = -32.234492396 Solving 6.25 + x = -32.234492396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -32.234492396 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -32.234492396 + -6.25 x = -32.234492396 + -6.25 Combine like terms: -32.234492396 + -6.25 = -38.484492396 x = -38.484492396 Simplifying x = -38.484492396Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.984492396, -38.484492396}
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