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Simplifying x2 + -1200x + -3025 = 0 Reorder the terms: -3025 + -1200x + x2 = 0 Solving -3025 + -1200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3025' to each side of the equation. -3025 + -1200x + 3025 + x2 = 0 + 3025 Reorder the terms: -3025 + 3025 + -1200x + x2 = 0 + 3025 Combine like terms: -3025 + 3025 = 0 0 + -1200x + x2 = 0 + 3025 -1200x + x2 = 0 + 3025 Combine like terms: 0 + 3025 = 3025 -1200x + x2 = 3025 The x term is -1200x. Take half its coefficient (-600). Square it (360000) and add it to both sides. Add '360000' to each side of the equation. -1200x + 360000 + x2 = 3025 + 360000 Reorder the terms: 360000 + -1200x + x2 = 3025 + 360000 Combine like terms: 3025 + 360000 = 363025 360000 + -1200x + x2 = 363025 Factor a perfect square on the left side: (x + -600)(x + -600) = 363025 Calculate the square root of the right side: 602.515559965 Break this problem into two subproblems by setting (x + -600) equal to 602.515559965 and -602.515559965.Subproblem 1
x + -600 = 602.515559965 Simplifying x + -600 = 602.515559965 Reorder the terms: -600 + x = 602.515559965 Solving -600 + x = 602.515559965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = 602.515559965 + 600 Combine like terms: -600 + 600 = 0 0 + x = 602.515559965 + 600 x = 602.515559965 + 600 Combine like terms: 602.515559965 + 600 = 1202.515559965 x = 1202.515559965 Simplifying x = 1202.515559965Subproblem 2
x + -600 = -602.515559965 Simplifying x + -600 = -602.515559965 Reorder the terms: -600 + x = -602.515559965 Solving -600 + x = -602.515559965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '600' to each side of the equation. -600 + 600 + x = -602.515559965 + 600 Combine like terms: -600 + 600 = 0 0 + x = -602.515559965 + 600 x = -602.515559965 + 600 Combine like terms: -602.515559965 + 600 = -2.515559965 x = -2.515559965 Simplifying x = -2.515559965Solution
The solution to the problem is based on the solutions from the subproblems. x = {1202.515559965, -2.515559965}
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