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Simplifying 0.60x(x + 50) + 0.80x = 79 Reorder the terms: 0.60x(50 + x) + 0.80x = 79 (50 * 0.60x + x * 0.60x) + 0.80x = 79 (30x + 0.60x2) + 0.80x = 79 Reorder the terms: 30x + 0.80x + 0.60x2 = 79 Combine like terms: 30x + 0.80x = 30.8x 30.8x + 0.60x2 = 79 Solving 30.8x + 0.60x2 = 79 Solving for variable 'x'. Reorder the terms: -79 + 30.8x + 0.60x2 = 79 + -79 Combine like terms: 79 + -79 = 0 -79 + 30.8x + 0.60x2 = 0 Begin completing the square. Divide all terms by 0.60 the coefficient of the squared term: Divide each side by '0.60'. -131.6666667 + 51.33333333x + x2 = 0 Move the constant term to the right: Add '131.6666667' to each side of the equation. -131.6666667 + 51.33333333x + 131.6666667 + x2 = 0 + 131.6666667 Reorder the terms: -131.6666667 + 131.6666667 + 51.33333333x + x2 = 0 + 131.6666667 Combine like terms: -131.6666667 + 131.6666667 = 0.0000000 0.0000000 + 51.33333333x + x2 = 0 + 131.6666667 51.33333333x + x2 = 0 + 131.6666667 Combine like terms: 0 + 131.6666667 = 131.6666667 51.33333333x + x2 = 131.6666667 The x term is 51.33333333x. Take half its coefficient (25.66666667). Square it (658.7777779) and add it to both sides. Add '658.7777779' to each side of the equation. 51.33333333x + 658.7777779 + x2 = 131.6666667 + 658.7777779 Reorder the terms: 658.7777779 + 51.33333333x + x2 = 131.6666667 + 658.7777779 Combine like terms: 131.6666667 + 658.7777779 = 790.4444446 658.7777779 + 51.33333333x + x2 = 790.4444446 Factor a perfect square on the left side: (x + 25.66666667)(x + 25.66666667) = 790.4444446 Calculate the square root of the right side: 28.114843848 Break this problem into two subproblems by setting (x + 25.66666667) equal to 28.114843848 and -28.114843848.Subproblem 1
x + 25.66666667 = 28.114843848 Simplifying x + 25.66666667 = 28.114843848 Reorder the terms: 25.66666667 + x = 28.114843848 Solving 25.66666667 + x = 28.114843848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.66666667' to each side of the equation. 25.66666667 + -25.66666667 + x = 28.114843848 + -25.66666667 Combine like terms: 25.66666667 + -25.66666667 = 0.00000000 0.00000000 + x = 28.114843848 + -25.66666667 x = 28.114843848 + -25.66666667 Combine like terms: 28.114843848 + -25.66666667 = 2.448177178 x = 2.448177178 Simplifying x = 2.448177178Subproblem 2
x + 25.66666667 = -28.114843848 Simplifying x + 25.66666667 = -28.114843848 Reorder the terms: 25.66666667 + x = -28.114843848 Solving 25.66666667 + x = -28.114843848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.66666667' to each side of the equation. 25.66666667 + -25.66666667 + x = -28.114843848 + -25.66666667 Combine like terms: 25.66666667 + -25.66666667 = 0.00000000 0.00000000 + x = -28.114843848 + -25.66666667 x = -28.114843848 + -25.66666667 Combine like terms: -28.114843848 + -25.66666667 = -53.781510518 x = -53.781510518 Simplifying x = -53.781510518Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.448177178, -53.781510518}
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