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Simplifying 9x2 + -100x + 2 = 0 Reorder the terms: 2 + -100x + 9x2 = 0 Solving 2 + -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'. 0.2222222222 + -11.11111111x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -11.11111111x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -11.11111111x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -11.11111111x + x2 = 0 + -0.2222222222 -11.11111111x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -11.11111111x + x2 = -0.2222222222 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 = -0.2222222222 + 30.86419752 Reorder the terms: 30.86419752 + -11.11111111x + x2 = -0.2222222222 + 30.86419752 Combine like terms: -0.2222222222 + 30.86419752 = 30.6419752978 30.86419752 + -11.11111111x + x2 = 30.6419752978 Factor a perfect square on the left side: (x + -5.555555555)(x + -5.555555555) = 30.6419752978 Calculate the square root of the right side: 5.535519424 Break this problem into two subproblems by setting (x + -5.555555555) equal to 5.535519424 and -5.535519424.Subproblem 1
x + -5.555555555 = 5.535519424 Simplifying x + -5.555555555 = 5.535519424 Reorder the terms: -5.555555555 + x = 5.535519424 Solving -5.555555555 + x = 5.535519424 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 = 5.535519424 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = 5.535519424 + 5.555555555 x = 5.535519424 + 5.555555555 Combine like terms: 5.535519424 + 5.555555555 = 11.091074979 x = 11.091074979 Simplifying x = 11.091074979Subproblem 2
x + -5.555555555 = -5.535519424 Simplifying x + -5.555555555 = -5.535519424 Reorder the terms: -5.555555555 + x = -5.535519424 Solving -5.555555555 + x = -5.535519424 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 = -5.535519424 + 5.555555555 Combine like terms: -5.555555555 + 5.555555555 = 0.000000000 0.000000000 + x = -5.535519424 + 5.555555555 x = -5.535519424 + 5.555555555 Combine like terms: -5.535519424 + 5.555555555 = 0.020036131 x = 0.020036131 Simplifying x = 0.020036131Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.091074979, 0.020036131}
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