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Simplifying 9x2 + -1x = 2000 Reorder the terms: -1x + 9x2 = 2000 Solving -1x + 9x2 = 2000 Solving for variable 'x'. Reorder the terms: -2000 + -1x + 9x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + -1x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -222.2222222 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '222.2222222' to each side of the equation. -222.2222222 + -0.1111111111x + 222.2222222 + x2 = 0 + 222.2222222 Reorder the terms: -222.2222222 + 222.2222222 + -0.1111111111x + x2 = 0 + 222.2222222 Combine like terms: -222.2222222 + 222.2222222 = 0.0000000 0.0000000 + -0.1111111111x + x2 = 0 + 222.2222222 -0.1111111111x + x2 = 0 + 222.2222222 Combine like terms: 0 + 222.2222222 = 222.2222222 -0.1111111111x + x2 = 222.2222222 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 222.2222222 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 222.2222222 + 0.003086419752 Combine like terms: 222.2222222 + 0.003086419752 = 222.225308619752 0.003086419752 + -0.1111111111x + x2 = 222.225308619752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 222.225308619752 Calculate the square root of the right side: 14.907223371 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 14.907223371 and -14.907223371.Subproblem 1
x + -0.05555555555 = 14.907223371 Simplifying x + -0.05555555555 = 14.907223371 Reorder the terms: -0.05555555555 + x = 14.907223371 Solving -0.05555555555 + x = 14.907223371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 14.907223371 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 14.907223371 + 0.05555555555 x = 14.907223371 + 0.05555555555 Combine like terms: 14.907223371 + 0.05555555555 = 14.96277892655 x = 14.96277892655 Simplifying x = 14.96277892655Subproblem 2
x + -0.05555555555 = -14.907223371 Simplifying x + -0.05555555555 = -14.907223371 Reorder the terms: -0.05555555555 + x = -14.907223371 Solving -0.05555555555 + x = -14.907223371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -14.907223371 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -14.907223371 + 0.05555555555 x = -14.907223371 + 0.05555555555 Combine like terms: -14.907223371 + 0.05555555555 = -14.85166781545 x = -14.85166781545 Simplifying x = -14.85166781545Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.96277892655, -14.85166781545}
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