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Simplifying 6x2 + 41x + -60 = 0 Reorder the terms: -60 + 41x + 6x2 = 0 Solving -60 + 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'. -10 + 6.833333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 6.833333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 6.833333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 6.833333333x + x2 = 0 + 10 6.833333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 6.833333333x + x2 = 10 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 = 10 + 11.67361111 Reorder the terms: 11.67361111 + 6.833333333x + x2 = 10 + 11.67361111 Combine like terms: 10 + 11.67361111 = 21.67361111 11.67361111 + 6.833333333x + x2 = 21.67361111 Factor a perfect square on the left side: (x + 3.416666667)(x + 3.416666667) = 21.67361111 Calculate the square root of the right side: 4.655492574 Break this problem into two subproblems by setting (x + 3.416666667) equal to 4.655492574 and -4.655492574.Subproblem 1
x + 3.416666667 = 4.655492574 Simplifying x + 3.416666667 = 4.655492574 Reorder the terms: 3.416666667 + x = 4.655492574 Solving 3.416666667 + x = 4.655492574 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 = 4.655492574 + -3.416666667 Combine like terms: 3.416666667 + -3.416666667 = 0.000000000 0.000000000 + x = 4.655492574 + -3.416666667 x = 4.655492574 + -3.416666667 Combine like terms: 4.655492574 + -3.416666667 = 1.238825907 x = 1.238825907 Simplifying x = 1.238825907Subproblem 2
x + 3.416666667 = -4.655492574 Simplifying x + 3.416666667 = -4.655492574 Reorder the terms: 3.416666667 + x = -4.655492574 Solving 3.416666667 + x = -4.655492574 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 = -4.655492574 + -3.416666667 Combine like terms: 3.416666667 + -3.416666667 = 0.000000000 0.000000000 + x = -4.655492574 + -3.416666667 x = -4.655492574 + -3.416666667 Combine like terms: -4.655492574 + -3.416666667 = -8.072159241 x = -8.072159241 Simplifying x = -8.072159241Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.238825907, -8.072159241}
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