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Simplifying x(x) + 11x + 6 = 0 Multiply x * x x2 + 11x + 6 = 0 Reorder the terms: 6 + 11x + x2 = 0 Solving 6 + 11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 11x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 11x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 11x + x2 = 0 + -6 11x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 11x + x2 = -6 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -6 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -6 + 30.25 Combine like terms: -6 + 30.25 = 24.25 30.25 + 11x + x2 = 24.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 5.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 5.5 = 4.924428901 Simplifying x + 5.5 = 4.924428901 Reorder the terms: 5.5 + x = 4.924428901 Solving 5.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 4.924428901 + -5.5 x = 4.924428901 + -5.5 Combine like terms: 4.924428901 + -5.5 = -0.575571099 x = -0.575571099 Simplifying x = -0.575571099Subproblem 2
x + 5.5 = -4.924428901 Simplifying x + 5.5 = -4.924428901 Reorder the terms: 5.5 + x = -4.924428901 Solving 5.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -4.924428901 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -4.924428901 + -5.5 x = -4.924428901 + -5.5 Combine like terms: -4.924428901 + -5.5 = -10.424428901 x = -10.424428901 Simplifying x = -10.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.575571099, -10.424428901}
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