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Simplifying 60x2 + -41x = 8 Reorder the terms: -41x + 60x2 = 8 Solving -41x + 60x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -41x + 60x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -41x + 60x2 = 0 Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.1333333333 + -0.6833333333x + x2 = 0 Move the constant term to the right: Add '0.1333333333' to each side of the equation. -0.1333333333 + -0.6833333333x + 0.1333333333 + x2 = 0 + 0.1333333333 Reorder the terms: -0.1333333333 + 0.1333333333 + -0.6833333333x + x2 = 0 + 0.1333333333 Combine like terms: -0.1333333333 + 0.1333333333 = 0.0000000000 0.0000000000 + -0.6833333333x + x2 = 0 + 0.1333333333 -0.6833333333x + x2 = 0 + 0.1333333333 Combine like terms: 0 + 0.1333333333 = 0.1333333333 -0.6833333333x + x2 = 0.1333333333 The x term is -0.6833333333x. Take half its coefficient (-0.3416666667). Square it (0.1167361111) and add it to both sides. Add '0.1167361111' to each side of the equation. -0.6833333333x + 0.1167361111 + x2 = 0.1333333333 + 0.1167361111 Reorder the terms: 0.1167361111 + -0.6833333333x + x2 = 0.1333333333 + 0.1167361111 Combine like terms: 0.1333333333 + 0.1167361111 = 0.2500694444 0.1167361111 + -0.6833333333x + x2 = 0.2500694444 Factor a perfect square on the left side: (x + -0.3416666667)(x + -0.3416666667) = 0.2500694444 Calculate the square root of the right side: 0.50006944 Break this problem into two subproblems by setting (x + -0.3416666667) equal to 0.50006944 and -0.50006944.Subproblem 1
x + -0.3416666667 = 0.50006944 Simplifying x + -0.3416666667 = 0.50006944 Reorder the terms: -0.3416666667 + x = 0.50006944 Solving -0.3416666667 + x = 0.50006944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3416666667' to each side of the equation. -0.3416666667 + 0.3416666667 + x = 0.50006944 + 0.3416666667 Combine like terms: -0.3416666667 + 0.3416666667 = 0.0000000000 0.0000000000 + x = 0.50006944 + 0.3416666667 x = 0.50006944 + 0.3416666667 Combine like terms: 0.50006944 + 0.3416666667 = 0.8417361067 x = 0.8417361067 Simplifying x = 0.8417361067Subproblem 2
x + -0.3416666667 = -0.50006944 Simplifying x + -0.3416666667 = -0.50006944 Reorder the terms: -0.3416666667 + x = -0.50006944 Solving -0.3416666667 + x = -0.50006944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3416666667' to each side of the equation. -0.3416666667 + 0.3416666667 + x = -0.50006944 + 0.3416666667 Combine like terms: -0.3416666667 + 0.3416666667 = 0.0000000000 0.0000000000 + x = -0.50006944 + 0.3416666667 x = -0.50006944 + 0.3416666667 Combine like terms: -0.50006944 + 0.3416666667 = -0.1584027733 x = -0.1584027733 Simplifying x = -0.1584027733Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8417361067, -0.1584027733}
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