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Simplifying x2 + -490x + 3600 = 0 Reorder the terms: 3600 + -490x + x2 = 0 Solving 3600 + -490x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3600' to each side of the equation. 3600 + -490x + -3600 + x2 = 0 + -3600 Reorder the terms: 3600 + -3600 + -490x + x2 = 0 + -3600 Combine like terms: 3600 + -3600 = 0 0 + -490x + x2 = 0 + -3600 -490x + x2 = 0 + -3600 Combine like terms: 0 + -3600 = -3600 -490x + x2 = -3600 The x term is -490x. Take half its coefficient (-245). Square it (60025) and add it to both sides. Add '60025' to each side of the equation. -490x + 60025 + x2 = -3600 + 60025 Reorder the terms: 60025 + -490x + x2 = -3600 + 60025 Combine like terms: -3600 + 60025 = 56425 60025 + -490x + x2 = 56425 Factor a perfect square on the left side: (x + -245)(x + -245) = 56425 Calculate the square root of the right side: 237.539470404 Break this problem into two subproblems by setting (x + -245) equal to 237.539470404 and -237.539470404.Subproblem 1
x + -245 = 237.539470404 Simplifying x + -245 = 237.539470404 Reorder the terms: -245 + x = 237.539470404 Solving -245 + x = 237.539470404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + x = 237.539470404 + 245 Combine like terms: -245 + 245 = 0 0 + x = 237.539470404 + 245 x = 237.539470404 + 245 Combine like terms: 237.539470404 + 245 = 482.539470404 x = 482.539470404 Simplifying x = 482.539470404Subproblem 2
x + -245 = -237.539470404 Simplifying x + -245 = -237.539470404 Reorder the terms: -245 + x = -237.539470404 Solving -245 + x = -237.539470404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + x = -237.539470404 + 245 Combine like terms: -245 + 245 = 0 0 + x = -237.539470404 + 245 x = -237.539470404 + 245 Combine like terms: -237.539470404 + 245 = 7.460529596 x = 7.460529596 Simplifying x = 7.460529596Solution
The solution to the problem is based on the solutions from the subproblems. x = {482.539470404, 7.460529596}
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