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Simplifying 6x2 + -35x + -11 = 0 Reorder the terms: -11 + -35x + 6x2 = 0 Solving -11 + -35x + 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 + -5.833333333x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -5.833333333x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -5.833333333x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -5.833333333x + x2 = 0 + 1.833333333 -5.833333333x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -5.833333333x + x2 = 1.833333333 The x term is -5.833333333x. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333x + 8.506944446 + x2 = 1.833333333 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333x + x2 = 1.833333333 + 8.506944446 Combine like terms: 1.833333333 + 8.506944446 = 10.340277779 8.506944446 + -5.833333333x + x2 = 10.340277779 Factor a perfect square on the left side: (x + -2.916666667)(x + -2.916666667) = 10.340277779 Calculate the square root of the right side: 3.21563023 Break this problem into two subproblems by setting (x + -2.916666667) equal to 3.21563023 and -3.21563023.Subproblem 1
x + -2.916666667 = 3.21563023 Simplifying x + -2.916666667 = 3.21563023 Reorder the terms: -2.916666667 + x = 3.21563023 Solving -2.916666667 + x = 3.21563023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = 3.21563023 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = 3.21563023 + 2.916666667 x = 3.21563023 + 2.916666667 Combine like terms: 3.21563023 + 2.916666667 = 6.132296897 x = 6.132296897 Simplifying x = 6.132296897Subproblem 2
x + -2.916666667 = -3.21563023 Simplifying x + -2.916666667 = -3.21563023 Reorder the terms: -2.916666667 + x = -3.21563023 Solving -2.916666667 + x = -3.21563023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + x = -3.21563023 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + x = -3.21563023 + 2.916666667 x = -3.21563023 + 2.916666667 Combine like terms: -3.21563023 + 2.916666667 = -0.298963563 x = -0.298963563 Simplifying x = -0.298963563Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.132296897, -0.298963563}
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