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Simplifying 2x2 + 4x + -999996 = 0 Reorder the terms: -999996 + 4x + 2x2 = 0 Solving -999996 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-499998 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-499998 + 2x + x2)' equal to zero and attempt to solve: Simplifying -499998 + 2x + x2 = 0 Solving -499998 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '499998' to each side of the equation. -499998 + 2x + 499998 + x2 = 0 + 499998 Reorder the terms: -499998 + 499998 + 2x + x2 = 0 + 499998 Combine like terms: -499998 + 499998 = 0 0 + 2x + x2 = 0 + 499998 2x + x2 = 0 + 499998 Combine like terms: 0 + 499998 = 499998 2x + x2 = 499998 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 = 499998 + 1 Reorder the terms: 1 + 2x + x2 = 499998 + 1 Combine like terms: 499998 + 1 = 499999 1 + 2x + x2 = 499999 Factor a perfect square on the left side: (x + 1)(x + 1) = 499999 Calculate the square root of the right side: 707.106074079 Break this problem into two subproblems by setting (x + 1) equal to 707.106074079 and -707.106074079.Subproblem 1
x + 1 = 707.106074079 Simplifying x + 1 = 707.106074079 Reorder the terms: 1 + x = 707.106074079 Solving 1 + x = 707.106074079 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 = 707.106074079 + -1 Combine like terms: 1 + -1 = 0 0 + x = 707.106074079 + -1 x = 707.106074079 + -1 Combine like terms: 707.106074079 + -1 = 706.106074079 x = 706.106074079 Simplifying x = 706.106074079Subproblem 2
x + 1 = -707.106074079 Simplifying x + 1 = -707.106074079 Reorder the terms: 1 + x = -707.106074079 Solving 1 + x = -707.106074079 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 = -707.106074079 + -1 Combine like terms: 1 + -1 = 0 0 + x = -707.106074079 + -1 x = -707.106074079 + -1 Combine like terms: -707.106074079 + -1 = -708.106074079 x = -708.106074079 Simplifying x = -708.106074079Solution
The solution to the problem is based on the solutions from the subproblems. x = {706.106074079, -708.106074079}Solution
x = {706.106074079, -708.106074079}
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