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Simplifying 13000 = 0.02x(1650 + -1x) 13000 = (1650 * 0.02x + -1x * 0.02x) 13000 = (33x + -0.02x2) Solving 13000 = 33x + -0.02x2 Solving for variable 'x'. Reorder the terms: 13000 + -33x + 0.02x2 = 33x + -33x + -0.02x2 + 0.02x2 Combine like terms: 33x + -33x = 0 13000 + -33x + 0.02x2 = 0 + -0.02x2 + 0.02x2 13000 + -33x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 13000 + -33x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 650000 + -1650x + x2 = 0 Move the constant term to the right: Add '-650000' to each side of the equation. 650000 + -1650x + -650000 + x2 = 0 + -650000 Reorder the terms: 650000 + -650000 + -1650x + x2 = 0 + -650000 Combine like terms: 650000 + -650000 = 0 0 + -1650x + x2 = 0 + -650000 -1650x + x2 = 0 + -650000 Combine like terms: 0 + -650000 = -650000 -1650x + x2 = -650000 The x term is -1650x. Take half its coefficient (-825). Square it (680625) and add it to both sides. Add '680625' to each side of the equation. -1650x + 680625 + x2 = -650000 + 680625 Reorder the terms: 680625 + -1650x + x2 = -650000 + 680625 Combine like terms: -650000 + 680625 = 30625 680625 + -1650x + x2 = 30625 Factor a perfect square on the left side: (x + -825)(x + -825) = 30625 Calculate the square root of the right side: 175 Break this problem into two subproblems by setting (x + -825) equal to 175 and -175.Subproblem 1
x + -825 = 175 Simplifying x + -825 = 175 Reorder the terms: -825 + x = 175 Solving -825 + x = 175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = 175 + 825 Combine like terms: -825 + 825 = 0 0 + x = 175 + 825 x = 175 + 825 Combine like terms: 175 + 825 = 1000 x = 1000 Simplifying x = 1000Subproblem 2
x + -825 = -175 Simplifying x + -825 = -175 Reorder the terms: -825 + x = -175 Solving -825 + x = -175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '825' to each side of the equation. -825 + 825 + x = -175 + 825 Combine like terms: -825 + 825 = 0 0 + x = -175 + 825 x = -175 + 825 Combine like terms: -175 + 825 = 650 x = 650 Simplifying x = 650Solution
The solution to the problem is based on the solutions from the subproblems. x = {1000, 650}
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