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Simplifying x2 + 450x + -30000 = 0 Reorder the terms: -30000 + 450x + x2 = 0 Solving -30000 + 450x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30000' to each side of the equation. -30000 + 450x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + 450x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + 450x + x2 = 0 + 30000 450x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 450x + x2 = 30000 The x term is 450x. Take half its coefficient (225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. 450x + 50625 + x2 = 30000 + 50625 Reorder the terms: 50625 + 450x + x2 = 30000 + 50625 Combine like terms: 30000 + 50625 = 80625 50625 + 450x + x2 = 80625 Factor a perfect square on the left side: (x + 225)(x + 225) = 80625 Calculate the square root of the right side: 283.94541729 Break this problem into two subproblems by setting (x + 225) equal to 283.94541729 and -283.94541729.Subproblem 1
x + 225 = 283.94541729 Simplifying x + 225 = 283.94541729 Reorder the terms: 225 + x = 283.94541729 Solving 225 + x = 283.94541729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-225' to each side of the equation. 225 + -225 + x = 283.94541729 + -225 Combine like terms: 225 + -225 = 0 0 + x = 283.94541729 + -225 x = 283.94541729 + -225 Combine like terms: 283.94541729 + -225 = 58.94541729 x = 58.94541729 Simplifying x = 58.94541729Subproblem 2
x + 225 = -283.94541729 Simplifying x + 225 = -283.94541729 Reorder the terms: 225 + x = -283.94541729 Solving 225 + x = -283.94541729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-225' to each side of the equation. 225 + -225 + x = -283.94541729 + -225 Combine like terms: 225 + -225 = 0 0 + x = -283.94541729 + -225 x = -283.94541729 + -225 Combine like terms: -283.94541729 + -225 = -508.94541729 x = -508.94541729 Simplifying x = -508.94541729Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.94541729, -508.94541729}
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