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Simplifying 3x * 3x + 11x + -4 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + 11x + -4 = 0 Multiply 3 * 3 9x * x + 11x + -4 = 0 Multiply x * x 9x2 + 11x + -4 = 0 Reorder the terms: -4 + 11x + 9x2 = 0 Solving -4 + 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'. -0.4444444444 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 1.222222222x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 1.222222222x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 1.222222222x + x2 = 0 + 0.4444444444 1.222222222x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 1.222222222x + x2 = 0.4444444444 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 = 0.4444444444 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 0.4444444444 + 0.3734567900 Combine like terms: 0.4444444444 + 0.3734567900 = 0.8179012344 0.3734567900 + 1.222222222x + x2 = 0.8179012344 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 0.8179012344 Calculate the square root of the right side: 0.904378922 Break this problem into two subproblems by setting (x + 0.611111111) equal to 0.904378922 and -0.904378922.Subproblem 1
x + 0.611111111 = 0.904378922 Simplifying x + 0.611111111 = 0.904378922 Reorder the terms: 0.611111111 + x = 0.904378922 Solving 0.611111111 + x = 0.904378922 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 = 0.904378922 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 0.904378922 + -0.611111111 x = 0.904378922 + -0.611111111 Combine like terms: 0.904378922 + -0.611111111 = 0.293267811 x = 0.293267811 Simplifying x = 0.293267811Subproblem 2
x + 0.611111111 = -0.904378922 Simplifying x + 0.611111111 = -0.904378922 Reorder the terms: 0.611111111 + x = -0.904378922 Solving 0.611111111 + x = -0.904378922 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 = -0.904378922 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -0.904378922 + -0.611111111 x = -0.904378922 + -0.611111111 Combine like terms: -0.904378922 + -0.611111111 = -1.515490033 x = -1.515490033 Simplifying x = -1.515490033Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293267811, -1.515490033}
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