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Simplifying 3495 = 0.05X2 + -45X + 12000 Reorder the terms: 3495 = 12000 + -45X + 0.05X2 Solving 3495 = 12000 + -45X + 0.05X2 Solving for variable 'X'. Combine like terms: 3495 + -12000 = -8505 -8505 + 45X + -0.05X2 = 12000 + -45X + 0.05X2 + -12000 + 45X + -0.05X2 Reorder the terms: -8505 + 45X + -0.05X2 = 12000 + -12000 + -45X + 45X + 0.05X2 + -0.05X2 Combine like terms: 12000 + -12000 = 0 -8505 + 45X + -0.05X2 = 0 + -45X + 45X + 0.05X2 + -0.05X2 -8505 + 45X + -0.05X2 = -45X + 45X + 0.05X2 + -0.05X2 Combine like terms: -45X + 45X = 0 -8505 + 45X + -0.05X2 = 0 + 0.05X2 + -0.05X2 -8505 + 45X + -0.05X2 = 0.05X2 + -0.05X2 Combine like terms: 0.05X2 + -0.05X2 = 0.00 -8505 + 45X + -0.05X2 = 0.00 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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