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Simplifying 6x2 + 66x + 11 = 0 Reorder the terms: 11 + 66x + 6x2 = 0 Solving 11 + 66x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + 11x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + 11x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + 11x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + 11x + x2 = 0 + -1.833333333 11x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 11x + x2 = -1.833333333 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 = -1.833333333 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -1.833333333 + 30.25 Combine like terms: -1.833333333 + 30.25 = 28.416666667 30.25 + 11x + x2 = 28.416666667 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 28.416666667 Calculate the square root of the right side: 5.330728531 Break this problem into two subproblems by setting (x + 5.5) equal to 5.330728531 and -5.330728531.Subproblem 1
x + 5.5 = 5.330728531 Simplifying x + 5.5 = 5.330728531 Reorder the terms: 5.5 + x = 5.330728531 Solving 5.5 + x = 5.330728531 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 = 5.330728531 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.330728531 + -5.5 x = 5.330728531 + -5.5 Combine like terms: 5.330728531 + -5.5 = -0.169271469 x = -0.169271469 Simplifying x = -0.169271469Subproblem 2
x + 5.5 = -5.330728531 Simplifying x + 5.5 = -5.330728531 Reorder the terms: 5.5 + x = -5.330728531 Solving 5.5 + x = -5.330728531 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 = -5.330728531 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.330728531 + -5.5 x = -5.330728531 + -5.5 Combine like terms: -5.330728531 + -5.5 = -10.830728531 x = -10.830728531 Simplifying x = -10.830728531Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.169271469, -10.830728531}
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