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Simplifying 24x2 + 11x + -80 = 0 Reorder the terms: -80 + 11x + 24x2 = 0 Solving -80 + 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'. -3.333333333 + 0.4583333333x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 0.4583333333x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 0.4583333333x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 0.4583333333x + x2 = 0 + 3.333333333 0.4583333333x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 0.4583333333x + x2 = 3.333333333 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 = 3.333333333 + 0.05251736113 Reorder the terms: 0.05251736113 + 0.4583333333x + x2 = 3.333333333 + 0.05251736113 Combine like terms: 3.333333333 + 0.05251736113 = 3.38585069413 0.05251736113 + 0.4583333333x + x2 = 3.38585069413 Factor a perfect square on the left side: (x + 0.2291666667)(x + 0.2291666667) = 3.38585069413 Calculate the square root of the right side: 1.840068122 Break this problem into two subproblems by setting (x + 0.2291666667) equal to 1.840068122 and -1.840068122.Subproblem 1
x + 0.2291666667 = 1.840068122 Simplifying x + 0.2291666667 = 1.840068122 Reorder the terms: 0.2291666667 + x = 1.840068122 Solving 0.2291666667 + x = 1.840068122 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 = 1.840068122 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = 1.840068122 + -0.2291666667 x = 1.840068122 + -0.2291666667 Combine like terms: 1.840068122 + -0.2291666667 = 1.6109014553 x = 1.6109014553 Simplifying x = 1.6109014553Subproblem 2
x + 0.2291666667 = -1.840068122 Simplifying x + 0.2291666667 = -1.840068122 Reorder the terms: 0.2291666667 + x = -1.840068122 Solving 0.2291666667 + x = -1.840068122 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 = -1.840068122 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = -1.840068122 + -0.2291666667 x = -1.840068122 + -0.2291666667 Combine like terms: -1.840068122 + -0.2291666667 = -2.0692347887 x = -2.0692347887 Simplifying x = -2.0692347887Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6109014553, -2.0692347887}
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