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Simplifying -0.03x(12000 + -1x) + 0.07 = 800 (12000 * -0.03x + -1x * -0.03x) + 0.07 = 800 (-360x + 0.03x2) + 0.07 = 800 Reorder the terms: 0.07 + -360x + 0.03x2 = 800 Solving 0.07 + -360x + 0.03x2 = 800 Solving for variable 'x'. Reorder the terms: 0.07 + -800 + -360x + 0.03x2 = 800 + -800 Combine like terms: 0.07 + -800 = -799.93 -799.93 + -360x + 0.03x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -799.93 + -360x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -26664.33333 + -12000x + x2 = 0 Move the constant term to the right: Add '26664.33333' to each side of the equation. -26664.33333 + -12000x + 26664.33333 + x2 = 0 + 26664.33333 Reorder the terms: -26664.33333 + 26664.33333 + -12000x + x2 = 0 + 26664.33333 Combine like terms: -26664.33333 + 26664.33333 = 0.00000 0.00000 + -12000x + x2 = 0 + 26664.33333 -12000x + x2 = 0 + 26664.33333 Combine like terms: 0 + 26664.33333 = 26664.33333 -12000x + x2 = 26664.33333 The x term is -12000x. Take half its coefficient (-6000). Square it (36000000) and add it to both sides. Add '36000000' to each side of the equation. -12000x + 36000000 + x2 = 26664.33333 + 36000000 Reorder the terms: 36000000 + -12000x + x2 = 26664.33333 + 36000000 Combine like terms: 26664.33333 + 36000000 = 36026664.33333 36000000 + -12000x + x2 = 36026664.33333 Factor a perfect square on the left side: (x + -6000)(x + -6000) = 36026664.33333 Calculate the square root of the right side: 6002.221616479 Break this problem into two subproblems by setting (x + -6000) equal to 6002.221616479 and -6002.221616479.Subproblem 1
x + -6000 = 6002.221616479 Simplifying x + -6000 = 6002.221616479 Reorder the terms: -6000 + x = 6002.221616479 Solving -6000 + x = 6002.221616479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = 6002.221616479 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = 6002.221616479 + 6000 x = 6002.221616479 + 6000 Combine like terms: 6002.221616479 + 6000 = 12002.221616479 x = 12002.221616479 Simplifying x = 12002.221616479Subproblem 2
x + -6000 = -6002.221616479 Simplifying x + -6000 = -6002.221616479 Reorder the terms: -6000 + x = -6002.221616479 Solving -6000 + x = -6002.221616479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6000' to each side of the equation. -6000 + 6000 + x = -6002.221616479 + 6000 Combine like terms: -6000 + 6000 = 0 0 + x = -6002.221616479 + 6000 x = -6002.221616479 + 6000 Combine like terms: -6002.221616479 + 6000 = -2.221616479 x = -2.221616479 Simplifying x = -2.221616479Solution
The solution to the problem is based on the solutions from the subproblems. x = {12002.221616479, -2.221616479}
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