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Simplifying x2 + 25x + -2000 = 0 Reorder the terms: -2000 + 25x + x2 = 0 Solving -2000 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 25x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 25x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 25x + x2 = 0 + 2000 25x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 25x + x2 = 2000 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 2000 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 2000 + 156.25 Combine like terms: 2000 + 156.25 = 2156.25 156.25 + 25x + x2 = 2156.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 2156.25 Calculate the square root of the right side: 46.435439053 Break this problem into two subproblems by setting (x + 12.5) equal to 46.435439053 and -46.435439053.Subproblem 1
x + 12.5 = 46.435439053 Simplifying x + 12.5 = 46.435439053 Reorder the terms: 12.5 + x = 46.435439053 Solving 12.5 + x = 46.435439053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 46.435439053 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 46.435439053 + -12.5 x = 46.435439053 + -12.5 Combine like terms: 46.435439053 + -12.5 = 33.935439053 x = 33.935439053 Simplifying x = 33.935439053Subproblem 2
x + 12.5 = -46.435439053 Simplifying x + 12.5 = -46.435439053 Reorder the terms: 12.5 + x = -46.435439053 Solving 12.5 + x = -46.435439053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -46.435439053 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -46.435439053 + -12.5 x = -46.435439053 + -12.5 Combine like terms: -46.435439053 + -12.5 = -58.935439053 x = -58.935439053 Simplifying x = -58.935439053Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.935439053, -58.935439053}
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