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Simplifying 810000 = x2 + x Reorder the terms: 810000 = x + x2 Solving 810000 = x + x2 Solving for variable 'x'. Reorder the terms: 810000 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 810000 + -1x + -1x2 = 0 + x2 + -1x2 810000 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 810000 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -810000 + x + x2 = 0 Move the constant term to the right: Add '810000' to each side of the equation. -810000 + x + 810000 + x2 = 0 + 810000 Reorder the terms: -810000 + 810000 + x + x2 = 0 + 810000 Combine like terms: -810000 + 810000 = 0 0 + x + x2 = 0 + 810000 x + x2 = 0 + 810000 Combine like terms: 0 + 810000 = 810000 x + x2 = 810000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 810000 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 810000 + 0.25 Combine like terms: 810000 + 0.25 = 810000.25 1.25 + x2 = 810000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 810000.25 Calculate the square root of the right side: 900.000138889 Break this problem into two subproblems by setting (x + 0.5) equal to 900.000138889 and -900.000138889.Subproblem 1
x + 0.5 = 900.000138889 Simplifying x + 0.5 = 900.000138889 Reorder the terms: 0.5 + x = 900.000138889 Solving 0.5 + x = 900.000138889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 900.000138889 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 900.000138889 + -0.5 x = 900.000138889 + -0.5 Combine like terms: 900.000138889 + -0.5 = 899.500138889 x = 899.500138889 Simplifying x = 899.500138889Subproblem 2
x + 0.5 = -900.000138889 Simplifying x + 0.5 = -900.000138889 Reorder the terms: 0.5 + x = -900.000138889 Solving 0.5 + x = -900.000138889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -900.000138889 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -900.000138889 + -0.5 x = -900.000138889 + -0.5 Combine like terms: -900.000138889 + -0.5 = -900.500138889 x = -900.500138889 Simplifying x = -900.500138889Solution
The solution to the problem is based on the solutions from the subproblems. x = {899.500138889, -900.500138889}
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