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Simplifying 800 = 9x + -0.01x2 Solving 800 = 9x + -0.01x2 Solving for variable 'x'. Reorder the terms: 800 + -9x + 0.01x2 = 9x + -9x + -0.01x2 + 0.01x2 Combine like terms: 9x + -9x = 0 800 + -9x + 0.01x2 = 0 + -0.01x2 + 0.01x2 800 + -9x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 800 + -9x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 80000 + -900x + x2 = 0 Move the constant term to the right: Add '-80000' to each side of the equation. 80000 + -900x + -80000 + x2 = 0 + -80000 Reorder the terms: 80000 + -80000 + -900x + x2 = 0 + -80000 Combine like terms: 80000 + -80000 = 0 0 + -900x + x2 = 0 + -80000 -900x + x2 = 0 + -80000 Combine like terms: 0 + -80000 = -80000 -900x + x2 = -80000 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 = -80000 + 202500 Reorder the terms: 202500 + -900x + x2 = -80000 + 202500 Combine like terms: -80000 + 202500 = 122500 202500 + -900x + x2 = 122500 Factor a perfect square on the left side: (x + -450)(x + -450) = 122500 Calculate the square root of the right side: 350 Break this problem into two subproblems by setting (x + -450) equal to 350 and -350.Subproblem 1
x + -450 = 350 Simplifying x + -450 = 350 Reorder the terms: -450 + x = 350 Solving -450 + x = 350 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 = 350 + 450 Combine like terms: -450 + 450 = 0 0 + x = 350 + 450 x = 350 + 450 Combine like terms: 350 + 450 = 800 x = 800 Simplifying x = 800Subproblem 2
x + -450 = -350 Simplifying x + -450 = -350 Reorder the terms: -450 + x = -350 Solving -450 + x = -350 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 = -350 + 450 Combine like terms: -450 + 450 = 0 0 + x = -350 + 450 x = -350 + 450 Combine like terms: -350 + 450 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {800, 100}
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