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Simplifying 2x2 + 4x + 4 = 999996 Reorder the terms: 4 + 4x + 2x2 = 999996 Solving 4 + 4x + 2x2 = 999996 Solving for variable 'x'. Reorder the terms: 4 + -999996 + 4x + 2x2 = 999996 + -999996 Combine like terms: 4 + -999996 = -999992 -999992 + 4x + 2x2 = 999996 + -999996 Combine like terms: 999996 + -999996 = 0 -999992 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-499996 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-499996 + 2x + x2)' equal to zero and attempt to solve: Simplifying -499996 + 2x + x2 = 0 Solving -499996 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '499996' to each side of the equation. -499996 + 2x + 499996 + x2 = 0 + 499996 Reorder the terms: -499996 + 499996 + 2x + x2 = 0 + 499996 Combine like terms: -499996 + 499996 = 0 0 + 2x + x2 = 0 + 499996 2x + x2 = 0 + 499996 Combine like terms: 0 + 499996 = 499996 2x + x2 = 499996 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 = 499996 + 1 Reorder the terms: 1 + 2x + x2 = 499996 + 1 Combine like terms: 499996 + 1 = 499997 1 + 2x + x2 = 499997 Factor a perfect square on the left side: (x + 1)(x + 1) = 499997 Calculate the square root of the right side: 707.104659863 Break this problem into two subproblems by setting (x + 1) equal to 707.104659863 and -707.104659863.Subproblem 1
x + 1 = 707.104659863 Simplifying x + 1 = 707.104659863 Reorder the terms: 1 + x = 707.104659863 Solving 1 + x = 707.104659863 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 = 707.104659863 + -1 Combine like terms: 1 + -1 = 0 0 + x = 707.104659863 + -1 x = 707.104659863 + -1 Combine like terms: 707.104659863 + -1 = 706.104659863 x = 706.104659863 Simplifying x = 706.104659863Subproblem 2
x + 1 = -707.104659863 Simplifying x + 1 = -707.104659863 Reorder the terms: 1 + x = -707.104659863 Solving 1 + x = -707.104659863 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 = -707.104659863 + -1 Combine like terms: 1 + -1 = 0 0 + x = -707.104659863 + -1 x = -707.104659863 + -1 Combine like terms: -707.104659863 + -1 = -708.104659863 x = -708.104659863 Simplifying x = -708.104659863Solution
The solution to the problem is based on the solutions from the subproblems. x = {706.104659863, -708.104659863}Solution
x = {706.104659863, -708.104659863}
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