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Simplifying 24x2 + -11x + -1 = 0 Reorder the terms: -1 + -11x + 24x2 = 0 Solving -1 + -11x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.04166666667 + -0.4583333333x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.4583333333x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.4583333333x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.4583333333x + x2 = 0 + 0.04166666667 -0.4583333333x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.4583333333x + x2 = 0.04166666667 The x term is -0.4583333333x. Take half its coefficient (-0.2291666667). Square it (0.05251736113) and add it to both sides. Add '0.05251736113' to each side of the equation. -0.4583333333x + 0.05251736113 + x2 = 0.04166666667 + 0.05251736113 Reorder the terms: 0.05251736113 + -0.4583333333x + x2 = 0.04166666667 + 0.05251736113 Combine like terms: 0.04166666667 + 0.05251736113 = 0.0941840278 0.05251736113 + -0.4583333333x + x2 = 0.0941840278 Factor a perfect square on the left side: (x + -0.2291666667)(x + -0.2291666667) = 0.0941840278 Calculate the square root of the right side: 0.306894164 Break this problem into two subproblems by setting (x + -0.2291666667) equal to 0.306894164 and -0.306894164.Subproblem 1
x + -0.2291666667 = 0.306894164 Simplifying x + -0.2291666667 = 0.306894164 Reorder the terms: -0.2291666667 + x = 0.306894164 Solving -0.2291666667 + x = 0.306894164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + x = 0.306894164 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = 0.306894164 + 0.2291666667 x = 0.306894164 + 0.2291666667 Combine like terms: 0.306894164 + 0.2291666667 = 0.5360608307 x = 0.5360608307 Simplifying x = 0.5360608307Subproblem 2
x + -0.2291666667 = -0.306894164 Simplifying x + -0.2291666667 = -0.306894164 Reorder the terms: -0.2291666667 + x = -0.306894164 Solving -0.2291666667 + x = -0.306894164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + x = -0.306894164 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + x = -0.306894164 + 0.2291666667 x = -0.306894164 + 0.2291666667 Combine like terms: -0.306894164 + 0.2291666667 = -0.0777274973 x = -0.0777274973 Simplifying x = -0.0777274973Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5360608307, -0.0777274973}
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