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Simplifying 9x2 + 173x + 818 = 0 Reorder the terms: 818 + 173x + 9x2 = 0 Solving 818 + 173x + 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'. 90.88888889 + 19.22222222x + x2 = 0 Move the constant term to the right: Add '-90.88888889' to each side of the equation. 90.88888889 + 19.22222222x + -90.88888889 + x2 = 0 + -90.88888889 Reorder the terms: 90.88888889 + -90.88888889 + 19.22222222x + x2 = 0 + -90.88888889 Combine like terms: 90.88888889 + -90.88888889 = 0.00000000 0.00000000 + 19.22222222x + x2 = 0 + -90.88888889 19.22222222x + x2 = 0 + -90.88888889 Combine like terms: 0 + -90.88888889 = -90.88888889 19.22222222x + x2 = -90.88888889 The x term is 19.22222222x. Take half its coefficient (9.61111111). Square it (92.37345677) and add it to both sides. Add '92.37345677' to each side of the equation. 19.22222222x + 92.37345677 + x2 = -90.88888889 + 92.37345677 Reorder the terms: 92.37345677 + 19.22222222x + x2 = -90.88888889 + 92.37345677 Combine like terms: -90.88888889 + 92.37345677 = 1.48456788 92.37345677 + 19.22222222x + x2 = 1.48456788 Factor a perfect square on the left side: (x + 9.61111111)(x + 9.61111111) = 1.48456788 Calculate the square root of the right side: 1.218428447 Break this problem into two subproblems by setting (x + 9.61111111) equal to 1.218428447 and -1.218428447.Subproblem 1
x + 9.61111111 = 1.218428447 Simplifying x + 9.61111111 = 1.218428447 Reorder the terms: 9.61111111 + x = 1.218428447 Solving 9.61111111 + x = 1.218428447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.61111111' to each side of the equation. 9.61111111 + -9.61111111 + x = 1.218428447 + -9.61111111 Combine like terms: 9.61111111 + -9.61111111 = 0.00000000 0.00000000 + x = 1.218428447 + -9.61111111 x = 1.218428447 + -9.61111111 Combine like terms: 1.218428447 + -9.61111111 = -8.392682663 x = -8.392682663 Simplifying x = -8.392682663Subproblem 2
x + 9.61111111 = -1.218428447 Simplifying x + 9.61111111 = -1.218428447 Reorder the terms: 9.61111111 + x = -1.218428447 Solving 9.61111111 + x = -1.218428447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.61111111' to each side of the equation. 9.61111111 + -9.61111111 + x = -1.218428447 + -9.61111111 Combine like terms: 9.61111111 + -9.61111111 = 0.00000000 0.00000000 + x = -1.218428447 + -9.61111111 x = -1.218428447 + -9.61111111 Combine like terms: -1.218428447 + -9.61111111 = -10.829539557 x = -10.829539557 Simplifying x = -10.829539557Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.392682663, -10.829539557}
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