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Simplifying 0.05x2 + -45x + 12000 = 3495 Reorder the terms: 12000 + -45x + 0.05x2 = 3495 Solving 12000 + -45x + 0.05x2 = 3495 Solving for variable 'x'. Reorder the terms: 12000 + -3495 + -45x + 0.05x2 = 3495 + -3495 Combine like terms: 12000 + -3495 = 8505 8505 + -45x + 0.05x2 = 3495 + -3495 Combine like terms: 3495 + -3495 = 0 8505 + -45x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 170100 + -900x + x2 = 0 Move the constant term to the right: Add '-170100' to each side of the equation. 170100 + -900x + -170100 + x2 = 0 + -170100 Reorder the terms: 170100 + -170100 + -900x + x2 = 0 + -170100 Combine like terms: 170100 + -170100 = 0 0 + -900x + x2 = 0 + -170100 -900x + x2 = 0 + -170100 Combine like terms: 0 + -170100 = -170100 -900x + x2 = -170100 The x term is -900x. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900x + 202500 + x2 = -170100 + 202500 Reorder the terms: 202500 + -900x + x2 = -170100 + 202500 Combine like terms: -170100 + 202500 = 32400 202500 + -900x + x2 = 32400 Factor a perfect square on the left side: (x + -450)(x + -450) = 32400 Calculate the square root of the right side: 180 Break this problem into two subproblems by setting (x + -450) equal to 180 and -180.Subproblem 1
x + -450 = 180 Simplifying x + -450 = 180 Reorder the terms: -450 + x = 180 Solving -450 + x = 180 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 180 + 450 Combine like terms: -450 + 450 = 0 0 + x = 180 + 450 x = 180 + 450 Combine like terms: 180 + 450 = 630 x = 630 Simplifying x = 630Subproblem 2
x + -450 = -180 Simplifying x + -450 = -180 Reorder the terms: -450 + x = -180 Solving -450 + x = -180 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = -180 + 450 Combine like terms: -450 + 450 = 0 0 + x = -180 + 450 x = -180 + 450 Combine like terms: -180 + 450 = 270 x = 270 Simplifying x = 270Solution
The solution to the problem is based on the solutions from the subproblems. x = {630, 270}
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