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Simplifying 2x2 + 12 = 2000x Reorder the terms: 12 + 2x2 = 2000x Solving 12 + 2x2 = 2000x Solving for variable 'x'. Reorder the terms: 12 + -2000x + 2x2 = 2000x + -2000x Combine like terms: 2000x + -2000x = 0 12 + -2000x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1000x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -1000x + x2)' equal to zero and attempt to solve: Simplifying 6 + -1000x + x2 = 0 Solving 6 + -1000x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -1000x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -1000x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1000x + x2 = 0 + -6 -1000x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1000x + x2 = -6 The x term is -1000x. Take half its coefficient (-500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. -1000x + 250000 + x2 = -6 + 250000 Reorder the terms: 250000 + -1000x + x2 = -6 + 250000 Combine like terms: -6 + 250000 = 249994 250000 + -1000x + x2 = 249994 Factor a perfect square on the left side: (x + -500)(x + -500) = 249994 Calculate the square root of the right side: 499.993999964 Break this problem into two subproblems by setting (x + -500) equal to 499.993999964 and -499.993999964.Subproblem 1
x + -500 = 499.993999964 Simplifying x + -500 = 499.993999964 Reorder the terms: -500 + x = 499.993999964 Solving -500 + x = 499.993999964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = 499.993999964 + 500 Combine like terms: -500 + 500 = 0 0 + x = 499.993999964 + 500 x = 499.993999964 + 500 Combine like terms: 499.993999964 + 500 = 999.993999964 x = 999.993999964 Simplifying x = 999.993999964Subproblem 2
x + -500 = -499.993999964 Simplifying x + -500 = -499.993999964 Reorder the terms: -500 + x = -499.993999964 Solving -500 + x = -499.993999964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '500' to each side of the equation. -500 + 500 + x = -499.993999964 + 500 Combine like terms: -500 + 500 = 0 0 + x = -499.993999964 + 500 x = -499.993999964 + 500 Combine like terms: -499.993999964 + 500 = 0.006000036 x = 0.006000036 Simplifying x = 0.006000036Solution
The solution to the problem is based on the solutions from the subproblems. x = {999.993999964, 0.006000036}Solution
x = {999.993999964, 0.006000036}
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