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Simplifying 9x2 + 11x + 3 = 0 Reorder the terms: 3 + 11x + 9x2 = 0 Solving 3 + 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'. 0.3333333333 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 1.222222222x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 1.222222222x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0 + -0.3333333333 1.222222222x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 1.222222222x + x2 = -0.3333333333 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 = -0.3333333333 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = -0.3333333333 + 0.3734567900 Combine like terms: -0.3333333333 + 0.3734567900 = 0.0401234567 0.3734567900 + 1.222222222x + x2 = 0.0401234567 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.0401234567 Calculate the square root of the right side: 0.200308404 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.200308404 and -0.200308404.Subproblem 1
x + 0.611111111 = 0.200308404 Simplifying x + 0.611111111 = 0.200308404 Reorder the terms: 0.611111111 + x = 0.200308404 Solving 0.611111111 + x = 0.200308404 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 = 0.200308404 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.200308404 + -0.611111111 x = 0.200308404 + -0.611111111 Combine like terms: 0.200308404 + -0.611111111 = -0.410802707 x = -0.410802707 Simplifying x = -0.410802707Subproblem 2
x + 0.611111111 = -0.200308404 Simplifying x + 0.611111111 = -0.200308404 Reorder the terms: 0.611111111 + x = -0.200308404 Solving 0.611111111 + x = -0.200308404 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 = -0.200308404 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.200308404 + -0.611111111 x = -0.200308404 + -0.611111111 Combine like terms: -0.200308404 + -0.611111111 = -0.811419515 x = -0.811419515 Simplifying x = -0.811419515Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.410802707, -0.811419515}
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