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Simplifying 0.05x2 + -45x + 12000 = 12920 Reorder the terms: 12000 + -45x + 0.05x2 = 12920 Solving 12000 + -45x + 0.05x2 = 12920 Solving for variable 'x'. Reorder the terms: 12000 + -12920 + -45x + 0.05x2 = 12920 + -12920 Combine like terms: 12000 + -12920 = -920 -920 + -45x + 0.05x2 = 12920 + -12920 Combine like terms: 12920 + -12920 = 0 -920 + -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'. -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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