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Simplifying 9x2 + -100x + -5 = 0 Reorder the terms: -5 + -100x + 9x2 = 0 Solving -5 + -100x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -11.11111111x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -11.11111111x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -11.11111111x + x2 = 0 + 0.5555555556 -11.11111111x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -11.11111111x + x2 = 0.5555555556 The x term is -11.11111111x. Take half its coefficient (-5.555555555). Square it (30.86419752) and add it to both sides. Add '30.86419752' to each side of the equation. -11.11111111x + 30.86419752 + x2 = 0.5555555556 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = 0.5555555556 + 30.86419752 Combine like terms: 0.5555555556 + 30.86419752 = 31.4197530756 30.86419752 + -11.11111111x + x2 = 31.4197530756 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = 31.4197530756 Calculate the square root of the right side: 5.605332557 Break this problem into two subproblems by setting (x + -5.555555555) equal to 5.605332557 and -5.605332557.Subproblem 1
x + -5.555555555 = 5.605332557 Simplifying x + -5.555555555 = 5.605332557 Reorder the terms: -5.555555555 + x = 5.605332557 Solving -5.555555555 + x = 5.605332557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = 5.605332557 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = 5.605332557 + 5.555555555 x = 5.605332557 + 5.555555555 Combine like terms: 5.605332557 + 5.555555555 = 11.160888112 x = 11.160888112 Simplifying x = 11.160888112Subproblem 2
x + -5.555555555 = -5.605332557 Simplifying x + -5.555555555 = -5.605332557 Reorder the terms: -5.555555555 + x = -5.605332557 Solving -5.555555555 + x = -5.605332557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.555555555' to each side of the equation. -5.555555555 + 5.555555555 + x = -5.605332557 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = -5.605332557 + 5.555555555 x = -5.605332557 + 5.555555555 Combine like terms: -5.605332557 + 5.555555555 = -0.049777002 x = -0.049777002 Simplifying x = -0.049777002Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.160888112, -0.049777002}
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