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Simplifying 3x(8x + 2) = 8 + -5x Reorder the terms: 3x(2 + 8x) = 8 + -5x (2 * 3x + 8x * 3x) = 8 + -5x (6x + 24x2) = 8 + -5x Solving 6x + 24x2 = 8 + -5x Solving for variable 'x'. Reorder the terms: -8 + 6x + 5x + 24x2 = 8 + -5x + -8 + 5x Combine like terms: 6x + 5x = 11x -8 + 11x + 24x2 = 8 + -5x + -8 + 5x Reorder the terms: -8 + 11x + 24x2 = 8 + -8 + -5x + 5x Combine like terms: 8 + -8 = 0 -8 + 11x + 24x2 = 0 + -5x + 5x -8 + 11x + 24x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -8 + 11x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.3333333333 + 0.4583333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.4583333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.4583333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.4583333333x + x2 = 0 + 0.3333333333 0.4583333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.4583333333x + x2 = 0.3333333333 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 = 0.3333333333 + 0.05251736113 Reorder the terms: 0.05251736113 + 0.4583333333x + x2 = 0.3333333333 + 0.05251736113 Combine like terms: 0.3333333333 + 0.05251736113 = 0.38585069443 0.05251736113 + 0.4583333333x + x2 = 0.38585069443 Factor a perfect square on the left side: (x + 0.2291666667)(x + 0.2291666667) = 0.38585069443 Calculate the square root of the right side: 0.621168813 Break this problem into two subproblems by setting (x + 0.2291666667) equal to 0.621168813 and -0.621168813.Subproblem 1
x + 0.2291666667 = 0.621168813 Simplifying x + 0.2291666667 = 0.621168813 Reorder the terms: 0.2291666667 + x = 0.621168813 Solving 0.2291666667 + x = 0.621168813 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 = 0.621168813 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = 0.621168813 + -0.2291666667 x = 0.621168813 + -0.2291666667 Combine like terms: 0.621168813 + -0.2291666667 = 0.3920021463 x = 0.3920021463 Simplifying x = 0.3920021463Subproblem 2
x + 0.2291666667 = -0.621168813 Simplifying x + 0.2291666667 = -0.621168813 Reorder the terms: 0.2291666667 + x = -0.621168813 Solving 0.2291666667 + x = -0.621168813 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 = -0.621168813 + -0.2291666667 Combine like terms: 0.2291666667 + -0.2291666667 = 0.0000000000 0.0000000000 + x = -0.621168813 + -0.2291666667 x = -0.621168813 + -0.2291666667 Combine like terms: -0.621168813 + -0.2291666667 = -0.8503354797 x = -0.8503354797 Simplifying x = -0.8503354797Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3920021463, -0.8503354797}
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