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Simplifying 9x2 + 10x + -20 = 0 Reorder the terms: -20 + 10x + 9x2 = 0 Solving -20 + 10x + 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'. -2.222222222 + 1.111111111x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.111111111x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.111111111x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.111111111x + x2 = 0 + 2.222222222 1.111111111x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.111111111x + x2 = 2.222222222 The x term is 1.111111111x. Take half its coefficient (0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. 1.111111111x + 0.3086419752 + x2 = 2.222222222 + 0.3086419752 Reorder the terms: 0.3086419752 + 1.111111111x + x2 = 2.222222222 + 0.3086419752 Combine like terms: 2.222222222 + 0.3086419752 = 2.5308641972 0.3086419752 + 1.111111111x + x2 = 2.5308641972 Factor a perfect square on the left side: (x + 0.5555555555)(x + 0.5555555555) = 2.5308641972 Calculate the square root of the right side: 1.590869007 Break this problem into two subproblems by setting (x + 0.5555555555) equal to 1.590869007 and -1.590869007.Subproblem 1
x + 0.5555555555 = 1.590869007 Simplifying x + 0.5555555555 = 1.590869007 Reorder the terms: 0.5555555555 + x = 1.590869007 Solving 0.5555555555 + x = 1.590869007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = 1.590869007 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = 1.590869007 + -0.5555555555 x = 1.590869007 + -0.5555555555 Combine like terms: 1.590869007 + -0.5555555555 = 1.0353134515 x = 1.0353134515 Simplifying x = 1.0353134515Subproblem 2
x + 0.5555555555 = -1.590869007 Simplifying x + 0.5555555555 = -1.590869007 Reorder the terms: 0.5555555555 + x = -1.590869007 Solving 0.5555555555 + x = -1.590869007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + x = -1.590869007 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + x = -1.590869007 + -0.5555555555 x = -1.590869007 + -0.5555555555 Combine like terms: -1.590869007 + -0.5555555555 = -2.1464245625 x = -2.1464245625 Simplifying x = -2.1464245625Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0353134515, -2.1464245625}
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