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Simplifying 6x2 + -41x + 54 = 0 Reorder the terms: 54 + -41x + 6x2 = 0 Solving 54 + -41x + 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'. 9 + -6.833333333x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -6.833333333x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -6.833333333x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -6.833333333x + x2 = 0 + -9 -6.833333333x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -6.833333333x + x2 = -9 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 = -9 + 11.67361111 Reorder the terms: 11.67361111 + -6.833333333x + x2 = -9 + 11.67361111 Combine like terms: -9 + 11.67361111 = 2.67361111 11.67361111 + -6.833333333x + x2 = 2.67361111 Factor a perfect square on the left side: (x + -3.416666667)(x + -3.416666667) = 2.67361111 Calculate the square root of the right side: 1.635118072 Break this problem into two subproblems by setting (x + -3.416666667) equal to 1.635118072 and -1.635118072.Subproblem 1
x + -3.416666667 = 1.635118072 Simplifying x + -3.416666667 = 1.635118072 Reorder the terms: -3.416666667 + x = 1.635118072 Solving -3.416666667 + x = 1.635118072 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 = 1.635118072 + 3.416666667 Combine like terms: -3.416666667 + 3.416666667 = 0.000000000 0.000000000 + x = 1.635118072 + 3.416666667 x = 1.635118072 + 3.416666667 Combine like terms: 1.635118072 + 3.416666667 = 5.051784739 x = 5.051784739 Simplifying x = 5.051784739Subproblem 2
x + -3.416666667 = -1.635118072 Simplifying x + -3.416666667 = -1.635118072 Reorder the terms: -3.416666667 + x = -1.635118072 Solving -3.416666667 + x = -1.635118072 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 = -1.635118072 + 3.416666667 Combine like terms: -3.416666667 + 3.416666667 = 0.000000000 0.000000000 + x = -1.635118072 + 3.416666667 x = -1.635118072 + 3.416666667 Combine like terms: -1.635118072 + 3.416666667 = 1.781548595 x = 1.781548595 Simplifying x = 1.781548595Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.051784739, 1.781548595}
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