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Simplifying 20 + 5x + -0.1x2 = 10x + -0.25x2 Solving 20 + 5x + -0.1x2 = 10x + -0.25x2 Solving for variable 'x'. Reorder the terms: 20 + 5x + -10x + -0.1x2 + 0.25x2 = 10x + -0.25x2 + -10x + 0.25x2 Combine like terms: 5x + -10x = -5x 20 + -5x + -0.1x2 + 0.25x2 = 10x + -0.25x2 + -10x + 0.25x2 Combine like terms: -0.1x2 + 0.25x2 = 0.15x2 20 + -5x + 0.15x2 = 10x + -0.25x2 + -10x + 0.25x2 Reorder the terms: 20 + -5x + 0.15x2 = 10x + -10x + -0.25x2 + 0.25x2 Combine like terms: 10x + -10x = 0 20 + -5x + 0.15x2 = 0 + -0.25x2 + 0.25x2 20 + -5x + 0.15x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 20 + -5x + 0.15x2 = 0.00 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. 133.3333333 + -33.33333333x + x2 = 0 Move the constant term to the right: Add '-133.3333333' to each side of the equation. 133.3333333 + -33.33333333x + -133.3333333 + x2 = 0 + -133.3333333 Reorder the terms: 133.3333333 + -133.3333333 + -33.33333333x + x2 = 0 + -133.3333333 Combine like terms: 133.3333333 + -133.3333333 = 0.0000000 0.0000000 + -33.33333333x + x2 = 0 + -133.3333333 -33.33333333x + x2 = 0 + -133.3333333 Combine like terms: 0 + -133.3333333 = -133.3333333 -33.33333333x + x2 = -133.3333333 The x term is -33.33333333x. Take half its coefficient (-16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. -33.33333333x + 277.7777779 + x2 = -133.3333333 + 277.7777779 Reorder the terms: 277.7777779 + -33.33333333x + x2 = -133.3333333 + 277.7777779 Combine like terms: -133.3333333 + 277.7777779 = 144.4444446 277.7777779 + -33.33333333x + x2 = 144.4444446 Factor a perfect square on the left side: (x + -16.66666667)(x + -16.66666667) = 144.4444446 Calculate the square root of the right side: 12.018504258 Break this problem into two subproblems by setting (x + -16.66666667) equal to 12.018504258 and -12.018504258.Subproblem 1
x + -16.66666667 = 12.018504258 Simplifying x + -16.66666667 = 12.018504258 Reorder the terms: -16.66666667 + x = 12.018504258 Solving -16.66666667 + x = 12.018504258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = 12.018504258 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = 12.018504258 + 16.66666667 x = 12.018504258 + 16.66666667 Combine like terms: 12.018504258 + 16.66666667 = 28.685170928 x = 28.685170928 Simplifying x = 28.685170928Subproblem 2
x + -16.66666667 = -12.018504258 Simplifying x + -16.66666667 = -12.018504258 Reorder the terms: -16.66666667 + x = -12.018504258 Solving -16.66666667 + x = -12.018504258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = -12.018504258 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = -12.018504258 + 16.66666667 x = -12.018504258 + 16.66666667 Combine like terms: -12.018504258 + 16.66666667 = 4.648162412 x = 4.648162412 Simplifying x = 4.648162412Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.685170928, 4.648162412}
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