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Simplifying -1x2 + 2200x + 2 = 0 Reorder the terms: 2 + 2200x + -1x2 = 0 Solving 2 + 2200x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2200x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2200x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2200x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2200x + x2 = 0 + 2 -2200x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2200x + x2 = 2 The x term is -2200x. Take half its coefficient (-1100). Square it (1210000) and add it to both sides. Add '1210000' to each side of the equation. -2200x + 1210000 + x2 = 2 + 1210000 Reorder the terms: 1210000 + -2200x + x2 = 2 + 1210000 Combine like terms: 2 + 1210000 = 1210002 1210000 + -2200x + x2 = 1210002 Factor a perfect square on the left side: (x + -1100)(x + -1100) = 1210002 Calculate the square root of the right side: 1100.000909091 Break this problem into two subproblems by setting (x + -1100) equal to 1100.000909091 and -1100.000909091.Subproblem 1
x + -1100 = 1100.000909091 Simplifying x + -1100 = 1100.000909091 Reorder the terms: -1100 + x = 1100.000909091 Solving -1100 + x = 1100.000909091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1100' to each side of the equation. -1100 + 1100 + x = 1100.000909091 + 1100 Combine like terms: -1100 + 1100 = 0 0 + x = 1100.000909091 + 1100 x = 1100.000909091 + 1100 Combine like terms: 1100.000909091 + 1100 = 2200.000909091 x = 2200.000909091 Simplifying x = 2200.000909091Subproblem 2
x + -1100 = -1100.000909091 Simplifying x + -1100 = -1100.000909091 Reorder the terms: -1100 + x = -1100.000909091 Solving -1100 + x = -1100.000909091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1100' to each side of the equation. -1100 + 1100 + x = -1100.000909091 + 1100 Combine like terms: -1100 + 1100 = 0 0 + x = -1100.000909091 + 1100 x = -1100.000909091 + 1100 Combine like terms: -1100.000909091 + 1100 = -0.000909091 x = -0.000909091 Simplifying x = -0.000909091Solution
The solution to the problem is based on the solutions from the subproblems. x = {2200.000909091, -0.000909091}
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