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Simplifying 18x2 + 121x + -22 = 0 Reorder the terms: -22 + 121x + 18x2 = 0 Solving -22 + 121x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.222222222 + 6.722222222x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 6.722222222x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 6.722222222x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 6.722222222x + x2 = 0 + 1.222222222 6.722222222x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 6.722222222x + x2 = 1.222222222 The x term is 6.722222222x. Take half its coefficient (3.361111111). Square it (11.29706790) and add it to both sides. Add '11.29706790' to each side of the equation. 6.722222222x + 11.29706790 + x2 = 1.222222222 + 11.29706790 Reorder the terms: 11.29706790 + 6.722222222x + x2 = 1.222222222 + 11.29706790 Combine like terms: 1.222222222 + 11.29706790 = 12.519290122 11.29706790 + 6.722222222x + x2 = 12.519290122 Factor a perfect square on the left side: (x + 3.361111111)(x + 3.361111111) = 12.519290122 Calculate the square root of the right side: 3.538260889 Break this problem into two subproblems by setting (x + 3.361111111) equal to 3.538260889 and -3.538260889.Subproblem 1
x + 3.361111111 = 3.538260889 Simplifying x + 3.361111111 = 3.538260889 Reorder the terms: 3.361111111 + x = 3.538260889 Solving 3.361111111 + x = 3.538260889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.361111111' to each side of the equation. 3.361111111 + -3.361111111 + x = 3.538260889 + -3.361111111 Combine like terms: 3.361111111 + -3.361111111 = 0.000000000 0.000000000 + x = 3.538260889 + -3.361111111 x = 3.538260889 + -3.361111111 Combine like terms: 3.538260889 + -3.361111111 = 0.177149778 x = 0.177149778 Simplifying x = 0.177149778Subproblem 2
x + 3.361111111 = -3.538260889 Simplifying x + 3.361111111 = -3.538260889 Reorder the terms: 3.361111111 + x = -3.538260889 Solving 3.361111111 + x = -3.538260889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.361111111' to each side of the equation. 3.361111111 + -3.361111111 + x = -3.538260889 + -3.361111111 Combine like terms: 3.361111111 + -3.361111111 = 0.000000000 0.000000000 + x = -3.538260889 + -3.361111111 x = -3.538260889 + -3.361111111 Combine like terms: -3.538260889 + -3.361111111 = -6.899372 x = -6.899372 Simplifying x = -6.899372Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.177149778, -6.899372}
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