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Simplifying -6x2 + 41x = 39 Reorder the terms: 41x + -6x2 = 39 Solving 41x + -6x2 = 39 Solving for variable 'x'. Reorder the terms: -39 + 41x + -6x2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 41x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 6.5 + -6.833333333x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -6.833333333x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -6.833333333x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -6.833333333x + x2 = 0 + -6.5 -6.833333333x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -6.833333333x + x2 = -6.5 The x term is -6.833333333x. Take half its coefficient (-3.416666667). Square it (11.67361111) and add it to both sides. Add '11.67361111' to each side of the equation. -6.833333333x + 11.67361111 + x2 = -6.5 + 11.67361111 Reorder the terms: 11.67361111 + -6.833333333x + x2 = -6.5 + 11.67361111 Combine like terms: -6.5 + 11.67361111 = 5.17361111 11.67361111 + -6.833333333x + x2 = 5.17361111 Factor a perfect square on the left side: (x + -3.416666667)(x + -3.416666667) = 5.17361111 Calculate the square root of the right side: 2.274557344 Break this problem into two subproblems by setting (x + -3.416666667) equal to 2.274557344 and -2.274557344.Subproblem 1
x + -3.416666667 = 2.274557344 Simplifying x + -3.416666667 = 2.274557344 Reorder the terms: -3.416666667 + x = 2.274557344 Solving -3.416666667 + x = 2.274557344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.416666667' to each side of the equation. -3.416666667 + 3.416666667 + x = 2.274557344 + 3.416666667 Combine like terms: -3.416666667 + 3.416666667 = 0.000000000 0.000000000 + x = 2.274557344 + 3.416666667 x = 2.274557344 + 3.416666667 Combine like terms: 2.274557344 + 3.416666667 = 5.691224011 x = 5.691224011 Simplifying x = 5.691224011Subproblem 2
x + -3.416666667 = -2.274557344 Simplifying x + -3.416666667 = -2.274557344 Reorder the terms: -3.416666667 + x = -2.274557344 Solving -3.416666667 + x = -2.274557344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.416666667' to each side of the equation. -3.416666667 + 3.416666667 + x = -2.274557344 + 3.416666667 Combine like terms: -3.416666667 + 3.416666667 = 0.000000000 0.000000000 + x = -2.274557344 + 3.416666667 x = -2.274557344 + 3.416666667 Combine like terms: -2.274557344 + 3.416666667 = 1.142109323 x = 1.142109323 Simplifying x = 1.142109323Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.691224011, 1.142109323}
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