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Simplifying 9x2 + 3 = 11x Reorder the terms: 3 + 9x2 = 11x Solving 3 + 9x2 = 11x Solving for variable 'x'. Reorder the terms: 3 + -11x + 9x2 = 11x + -11x Combine like terms: 11x + -11x = 0 3 + -11x + 9x2 = 0 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 = 0.811419515 x = 0.811419515 Simplifying x = 0.811419515Subproblem 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 = 0.410802707 x = 0.410802707 Simplifying x = 0.410802707Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.811419515, 0.410802707}
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