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Simplifying 0.60x + 0.40x(100 + -1x) = 50 0.60x + (100 * 0.40x + -1x * 0.40x) = 50 0.60x + (40x + -0.4x2) = 50 Combine like terms: 0.60x + 40x = 40.6x 40.6x + -0.4x2 = 50 Solving 40.6x + -0.4x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 40.6x + -0.4x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 40.6x + -0.4x2 = 0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 125 + -101.5x + x2 = 0 Move the constant term to the right: Add '-125' to each side of the equation. 125 + -101.5x + -125 + x2 = 0 + -125 Reorder the terms: 125 + -125 + -101.5x + x2 = 0 + -125 Combine like terms: 125 + -125 = 0 0 + -101.5x + x2 = 0 + -125 -101.5x + x2 = 0 + -125 Combine like terms: 0 + -125 = -125 -101.5x + x2 = -125 The x term is -101.5x. Take half its coefficient (-50.75). Square it (2575.5625) and add it to both sides. Add '2575.5625' to each side of the equation. -101.5x + 2575.5625 + x2 = -125 + 2575.5625 Reorder the terms: 2575.5625 + -101.5x + x2 = -125 + 2575.5625 Combine like terms: -125 + 2575.5625 = 2450.5625 2575.5625 + -101.5x + x2 = 2450.5625 Factor a perfect square on the left side: (x + -50.75)(x + -50.75) = 2450.5625 Calculate the square root of the right side: 49.503156465 Break this problem into two subproblems by setting (x + -50.75) equal to 49.503156465 and -49.503156465.Subproblem 1
x + -50.75 = 49.503156465 Simplifying x + -50.75 = 49.503156465 Reorder the terms: -50.75 + x = 49.503156465 Solving -50.75 + x = 49.503156465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.75' to each side of the equation. -50.75 + 50.75 + x = 49.503156465 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + x = 49.503156465 + 50.75 x = 49.503156465 + 50.75 Combine like terms: 49.503156465 + 50.75 = 100.253156465 x = 100.253156465 Simplifying x = 100.253156465Subproblem 2
x + -50.75 = -49.503156465 Simplifying x + -50.75 = -49.503156465 Reorder the terms: -50.75 + x = -49.503156465 Solving -50.75 + x = -49.503156465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50.75' to each side of the equation. -50.75 + 50.75 + x = -49.503156465 + 50.75 Combine like terms: -50.75 + 50.75 = 0.00 0.00 + x = -49.503156465 + 50.75 x = -49.503156465 + 50.75 Combine like terms: -49.503156465 + 50.75 = 1.246843535 x = 1.246843535 Simplifying x = 1.246843535Solution
The solution to the problem is based on the solutions from the subproblems. x = {100.253156465, 1.246843535}
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