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Simplifying 12920 = 0.05X2 + -45X + 12000 Reorder the terms: 12920 = 12000 + -45X + 0.05X2 Solving 12920 = 12000 + -45X + 0.05X2 Solving for variable 'X'. Combine like terms: 12920 + -12000 = 920 920 + 45X + -0.05X2 = 12000 + -45X + 0.05X2 + -12000 + 45X + -0.05X2 Reorder the terms: 920 + 45X + -0.05X2 = 12000 + -12000 + -45X + 45X + 0.05X2 + -0.05X2 Combine like terms: 12000 + -12000 = 0 920 + 45X + -0.05X2 = 0 + -45X + 45X + 0.05X2 + -0.05X2 920 + 45X + -0.05X2 = -45X + 45X + 0.05X2 + -0.05X2 Combine like terms: -45X + 45X = 0 920 + 45X + -0.05X2 = 0 + 0.05X2 + -0.05X2 920 + 45X + -0.05X2 = 0.05X2 + -0.05X2 Combine like terms: 0.05X2 + -0.05X2 = 0.00 920 + 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'. -18400 + -900X + X2 = 0 Move the constant term to the right: Add '18400' to each side of the equation. -18400 + -900X + 18400 + X2 = 0 + 18400 Reorder the terms: -18400 + 18400 + -900X + X2 = 0 + 18400 Combine like terms: -18400 + 18400 = 0 0 + -900X + X2 = 0 + 18400 -900X + X2 = 0 + 18400 Combine like terms: 0 + 18400 = 18400 -900X + X2 = 18400 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 = 18400 + 202500 Reorder the terms: 202500 + -900X + X2 = 18400 + 202500 Combine like terms: 18400 + 202500 = 220900 202500 + -900X + X2 = 220900 Factor a perfect square on the left side: (X + -450)(X + -450) = 220900 Calculate the square root of the right side: 470 Break this problem into two subproblems by setting (X + -450) equal to 470 and -470.Subproblem 1
X + -450 = 470 Simplifying X + -450 = 470 Reorder the terms: -450 + X = 470 Solving -450 + X = 470 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 = 470 + 450 Combine like terms: -450 + 450 = 0 0 + X = 470 + 450 X = 470 + 450 Combine like terms: 470 + 450 = 920 X = 920 Simplifying X = 920Subproblem 2
X + -450 = -470 Simplifying X + -450 = -470 Reorder the terms: -450 + X = -470 Solving -450 + X = -470 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 = -470 + 450 Combine like terms: -450 + 450 = 0 0 + X = -470 + 450 X = -470 + 450 Combine like terms: -470 + 450 = -20 X = -20 Simplifying X = -20Solution
The solution to the problem is based on the solutions from the subproblems. X = {920, -20}
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