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Simplifying 1600 = 12x + -0.02x2 Solving 1600 = 12x + -0.02x2 Solving for variable 'x'. Reorder the terms: 1600 + -12x + 0.02x2 = 12x + -12x + -0.02x2 + 0.02x2 Combine like terms: 12x + -12x = 0 1600 + -12x + 0.02x2 = 0 + -0.02x2 + 0.02x2 1600 + -12x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 1600 + -12x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 80000 + -600x + x2 = 0 Move the constant term to the right: Add '-80000' to each side of the equation. 80000 + -600x + -80000 + x2 = 0 + -80000 Reorder the terms: 80000 + -80000 + -600x + x2 = 0 + -80000 Combine like terms: 80000 + -80000 = 0 0 + -600x + x2 = 0 + -80000 -600x + x2 = 0 + -80000 Combine like terms: 0 + -80000 = -80000 -600x + x2 = -80000 The x term is -600x. Take half its coefficient (-300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. -600x + 90000 + x2 = -80000 + 90000 Reorder the terms: 90000 + -600x + x2 = -80000 + 90000 Combine like terms: -80000 + 90000 = 10000 90000 + -600x + x2 = 10000 Factor a perfect square on the left side: (x + -300)(x + -300) = 10000 Calculate the square root of the right side: 100 Break this problem into two subproblems by setting (x + -300) equal to 100 and -100.Subproblem 1
x + -300 = 100 Simplifying x + -300 = 100 Reorder the terms: -300 + x = 100 Solving -300 + x = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = 100 + 300 Combine like terms: -300 + 300 = 0 0 + x = 100 + 300 x = 100 + 300 Combine like terms: 100 + 300 = 400 x = 400 Simplifying x = 400Subproblem 2
x + -300 = -100 Simplifying x + -300 = -100 Reorder the terms: -300 + x = -100 Solving -300 + x = -100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '300' to each side of the equation. -300 + 300 + x = -100 + 300 Combine like terms: -300 + 300 = 0 0 + x = -100 + 300 x = -100 + 300 Combine like terms: -100 + 300 = 200 x = 200 Simplifying x = 200Solution
The solution to the problem is based on the solutions from the subproblems. x = {400, 200}
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