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Simplifying 9x2 + -11x + -2 = 0 Reorder the terms: -2 + -11x + 9x2 = 0 Solving -2 + -11x + 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 + -1.222222222x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1.222222222x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1.222222222x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1.222222222x + x2 = 0 + 0.2222222222 -1.222222222x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1.222222222x + x2 = 0.2222222222 The x term is -1.222222222x. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222x + 0.3734567900 + x2 = 0.2222222222 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x + x2 = 0.2222222222 + 0.3734567900 Combine like terms: 0.2222222222 + 0.3734567900 = 0.5956790122 0.3734567900 + -1.222222222x + x2 = 0.5956790122 Factor a perfect square on the left side: (x + -0.611111111)(x + -0.611111111) = 0.5956790122 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (x + -0.611111111) equal to 0.771802444 and -0.771802444.Subproblem 1
x + -0.611111111 = 0.771802444 Simplifying x + -0.611111111 = 0.771802444 Reorder the terms: -0.611111111 + x = 0.771802444 Solving -0.611111111 + x = 0.771802444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = 0.771802444 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = 0.771802444 + 0.611111111 x = 0.771802444 + 0.611111111 Combine like terms: 0.771802444 + 0.611111111 = 1.382913555 x = 1.382913555 Simplifying x = 1.382913555Subproblem 2
x + -0.611111111 = -0.771802444 Simplifying x + -0.611111111 = -0.771802444 Reorder the terms: -0.611111111 + x = -0.771802444 Solving -0.611111111 + x = -0.771802444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = -0.771802444 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = -0.771802444 + 0.611111111 x = -0.771802444 + 0.611111111 Combine like terms: -0.771802444 + 0.611111111 = -0.160691333 x = -0.160691333 Simplifying x = -0.160691333Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.382913555, -0.160691333}
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