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Simplifying 2x2 + -1000x + -5 = 0 Reorder the terms: -5 + -1000x + 2x2 = 0 Solving -5 + -1000x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -500x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -500x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -500x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -500x + x2 = 0 + 2.5 -500x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -500x + x2 = 2.5 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = 2.5 + 62500 Reorder the terms: 62500 + -500x + x2 = 2.5 + 62500 Combine like terms: 2.5 + 62500 = 62502.5 62500 + -500x + x2 = 62502.5 Factor a perfect square on the left side: (x + -250)(x + -250) = 62502.5 Calculate the square root of the right side: 250.00499995 Break this problem into two subproblems by setting (x + -250) equal to 250.00499995 and -250.00499995.Subproblem 1
x + -250 = 250.00499995 Simplifying x + -250 = 250.00499995 Reorder the terms: -250 + x = 250.00499995 Solving -250 + x = 250.00499995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 250.00499995 + 250 Combine like terms: -250 + 250 = 0 0 + x = 250.00499995 + 250 x = 250.00499995 + 250 Combine like terms: 250.00499995 + 250 = 500.00499995 x = 500.00499995 Simplifying x = 500.00499995Subproblem 2
x + -250 = -250.00499995 Simplifying x + -250 = -250.00499995 Reorder the terms: -250 + x = -250.00499995 Solving -250 + x = -250.00499995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -250.00499995 + 250 Combine like terms: -250 + 250 = 0 0 + x = -250.00499995 + 250 x = -250.00499995 + 250 Combine like terms: -250.00499995 + 250 = -0.00499995 x = -0.00499995 Simplifying x = -0.00499995Solution
The solution to the problem is based on the solutions from the subproblems. x = {500.00499995, -0.00499995}
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