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Simplifying x2 + 2400x + -480 = 0 Reorder the terms: -480 + 2400x + x2 = 0 Solving -480 + 2400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '480' to each side of the equation. -480 + 2400x + 480 + x2 = 0 + 480 Reorder the terms: -480 + 480 + 2400x + x2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 2400x + x2 = 0 + 480 2400x + x2 = 0 + 480 Combine like terms: 0 + 480 = 480 2400x + x2 = 480 The x term is 2400x. Take half its coefficient (1200). Square it (1440000) and add it to both sides. Add '1440000' to each side of the equation. 2400x + 1440000 + x2 = 480 + 1440000 Reorder the terms: 1440000 + 2400x + x2 = 480 + 1440000 Combine like terms: 480 + 1440000 = 1440480 1440000 + 2400x + x2 = 1440480 Factor a perfect square on the left side: (x + 1200)(x + 1200) = 1440480 Calculate the square root of the right side: 1200.199983336 Break this problem into two subproblems by setting (x + 1200) equal to 1200.199983336 and -1200.199983336.Subproblem 1
x + 1200 = 1200.199983336 Simplifying x + 1200 = 1200.199983336 Reorder the terms: 1200 + x = 1200.199983336 Solving 1200 + x = 1200.199983336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = 1200.199983336 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = 1200.199983336 + -1200 x = 1200.199983336 + -1200 Combine like terms: 1200.199983336 + -1200 = 0.199983336 x = 0.199983336 Simplifying x = 0.199983336Subproblem 2
x + 1200 = -1200.199983336 Simplifying x + 1200 = -1200.199983336 Reorder the terms: 1200 + x = -1200.199983336 Solving 1200 + x = -1200.199983336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1200' to each side of the equation. 1200 + -1200 + x = -1200.199983336 + -1200 Combine like terms: 1200 + -1200 = 0 0 + x = -1200.199983336 + -1200 x = -1200.199983336 + -1200 Combine like terms: -1200.199983336 + -1200 = -2400.199983336 x = -2400.199983336 Simplifying x = -2400.199983336Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.199983336, -2400.199983336}
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