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Simplifying 80x + 0.1x2 + -1(40x + 0.2x2 + 2000) = x Reorder the terms: 80x + 0.1x2 + -1(2000 + 40x + 0.2x2) = x 80x + 0.1x2 + (2000 * -1 + 40x * -1 + 0.2x2 * -1) = x 80x + 0.1x2 + (-2000 + -40x + -0.2x2) = x Reorder the terms: -2000 + 80x + -40x + 0.1x2 + -0.2x2 = x Combine like terms: 80x + -40x = 40x -2000 + 40x + 0.1x2 + -0.2x2 = x Combine like terms: 0.1x2 + -0.2x2 = -0.1x2 -2000 + 40x + -0.1x2 = x Solving -2000 + 40x + -0.1x2 = x Solving for variable 'x'. Reorder the terms: -2000 + 40x + -1x + -0.1x2 = x + -1x Combine like terms: 40x + -1x = 39x -2000 + 39x + -0.1x2 = x + -1x Combine like terms: x + -1x = 0 -2000 + 39x + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 20000 + -390x + x2 = 0 Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -390x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -390x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -390x + x2 = 0 + -20000 -390x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -390x + x2 = -20000 The x term is -390x. Take half its coefficient (-195). Square it (38025) and add it to both sides. Add '38025' to each side of the equation. -390x + 38025 + x2 = -20000 + 38025 Reorder the terms: 38025 + -390x + x2 = -20000 + 38025 Combine like terms: -20000 + 38025 = 18025 38025 + -390x + x2 = 18025 Factor a perfect square on the left side: (x + -195)(x + -195) = 18025 Calculate the square root of the right side: 134.257215821 Break this problem into two subproblems by setting (x + -195) equal to 134.257215821 and -134.257215821.Subproblem 1
x + -195 = 134.257215821 Simplifying x + -195 = 134.257215821 Reorder the terms: -195 + x = 134.257215821 Solving -195 + x = 134.257215821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '195' to each side of the equation. -195 + 195 + x = 134.257215821 + 195 Combine like terms: -195 + 195 = 0 0 + x = 134.257215821 + 195 x = 134.257215821 + 195 Combine like terms: 134.257215821 + 195 = 329.257215821 x = 329.257215821 Simplifying x = 329.257215821Subproblem 2
x + -195 = -134.257215821 Simplifying x + -195 = -134.257215821 Reorder the terms: -195 + x = -134.257215821 Solving -195 + x = -134.257215821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '195' to each side of the equation. -195 + 195 + x = -134.257215821 + 195 Combine like terms: -195 + 195 = 0 0 + x = -134.257215821 + 195 x = -134.257215821 + 195 Combine like terms: -134.257215821 + 195 = 60.742784179 x = 60.742784179 Simplifying x = 60.742784179Solution
The solution to the problem is based on the solutions from the subproblems. x = {329.257215821, 60.742784179}
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