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Simplifying x2 + 2x + -4998 = 0 Reorder the terms: -4998 + 2x + x2 = 0 Solving -4998 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4998' to each side of the equation. -4998 + 2x + 4998 + x2 = 0 + 4998 Reorder the terms: -4998 + 4998 + 2x + x2 = 0 + 4998 Combine like terms: -4998 + 4998 = 0 0 + 2x + x2 = 0 + 4998 2x + x2 = 0 + 4998 Combine like terms: 0 + 4998 = 4998 2x + x2 = 4998 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 = 4998 + 1 Reorder the terms: 1 + 2x + x2 = 4998 + 1 Combine like terms: 4998 + 1 = 4999 1 + 2x + x2 = 4999 Factor a perfect square on the left side: (x + 1)(x + 1) = 4999 Calculate the square root of the right side: 70.703606697 Break this problem into two subproblems by setting (x + 1) equal to 70.703606697 and -70.703606697.Subproblem 1
x + 1 = 70.703606697 Simplifying x + 1 = 70.703606697 Reorder the terms: 1 + x = 70.703606697 Solving 1 + x = 70.703606697 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 = 70.703606697 + -1 Combine like terms: 1 + -1 = 0 0 + x = 70.703606697 + -1 x = 70.703606697 + -1 Combine like terms: 70.703606697 + -1 = 69.703606697 x = 69.703606697 Simplifying x = 69.703606697Subproblem 2
x + 1 = -70.703606697 Simplifying x + 1 = -70.703606697 Reorder the terms: 1 + x = -70.703606697 Solving 1 + x = -70.703606697 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 = -70.703606697 + -1 Combine like terms: 1 + -1 = 0 0 + x = -70.703606697 + -1 x = -70.703606697 + -1 Combine like terms: -70.703606697 + -1 = -71.703606697 x = -71.703606697 Simplifying x = -71.703606697Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.703606697, -71.703606697}
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