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Simplifying x2 + 2x + -5764801 = 0 Reorder the terms: -5764801 + 2x + x2 = 0 Solving -5764801 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5764801' to each side of the equation. -5764801 + 2x + 5764801 + x2 = 0 + 5764801 Reorder the terms: -5764801 + 5764801 + 2x + x2 = 0 + 5764801 Combine like terms: -5764801 + 5764801 = 0 0 + 2x + x2 = 0 + 5764801 2x + x2 = 0 + 5764801 Combine like terms: 0 + 5764801 = 5764801 2x + x2 = 5764801 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5764801 + 1 Reorder the terms: 1 + 2x + x2 = 5764801 + 1 Combine like terms: 5764801 + 1 = 5764802 1 + 2x + x2 = 5764802 Factor a perfect square on the left side: (x + 1)(x + 1) = 5764802 Calculate the square root of the right side: 2401.000208247 Break this problem into two subproblems by setting (x + 1) equal to 2401.000208247 and -2401.000208247.Subproblem 1
x + 1 = 2401.000208247 Simplifying x + 1 = 2401.000208247 Reorder the terms: 1 + x = 2401.000208247 Solving 1 + x = 2401.000208247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2401.000208247 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2401.000208247 + -1 x = 2401.000208247 + -1 Combine like terms: 2401.000208247 + -1 = 2400.000208247 x = 2400.000208247 Simplifying x = 2400.000208247Subproblem 2
x + 1 = -2401.000208247 Simplifying x + 1 = -2401.000208247 Reorder the terms: 1 + x = -2401.000208247 Solving 1 + x = -2401.000208247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2401.000208247 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2401.000208247 + -1 x = -2401.000208247 + -1 Combine like terms: -2401.000208247 + -1 = -2402.000208247 x = -2402.000208247 Simplifying x = -2402.000208247Solution
The solution to the problem is based on the solutions from the subproblems. x = {2400.000208247, -2402.000208247}
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