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Simplifying 0 = -0.02x2 + 8x + -600 Reorder the terms: 0 = -600 + 8x + -0.02x2 Solving 0 = -600 + 8x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + 600 = 600 600 + -8x + 0.02x2 = -600 + 8x + -0.02x2 + 600 + -8x + 0.02x2 Reorder the terms: 600 + -8x + 0.02x2 = -600 + 600 + 8x + -8x + -0.02x2 + 0.02x2 Combine like terms: -600 + 600 = 0 600 + -8x + 0.02x2 = 0 + 8x + -8x + -0.02x2 + 0.02x2 600 + -8x + 0.02x2 = 8x + -8x + -0.02x2 + 0.02x2 Combine like terms: 8x + -8x = 0 600 + -8x + 0.02x2 = 0 + -0.02x2 + 0.02x2 600 + -8x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 600 + -8x + 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'. 30000 + -400x + x2 = 0 Move the constant term to the right: Add '-30000' to each side of the equation. 30000 + -400x + -30000 + x2 = 0 + -30000 Reorder the terms: 30000 + -30000 + -400x + x2 = 0 + -30000 Combine like terms: 30000 + -30000 = 0 0 + -400x + x2 = 0 + -30000 -400x + x2 = 0 + -30000 Combine like terms: 0 + -30000 = -30000 -400x + x2 = -30000 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -30000 + 40000 Reorder the terms: 40000 + -400x + x2 = -30000 + 40000 Combine like terms: -30000 + 40000 = 10000 40000 + -400x + x2 = 10000 Factor a perfect square on the left side: (x + -200)(x + -200) = 10000 Calculate the square root of the right side: 100 Break this problem into two subproblems by setting (x + -200) equal to 100 and -100.Subproblem 1
x + -200 = 100 Simplifying x + -200 = 100 Reorder the terms: -200 + x = 100 Solving -200 + x = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 100 + 200 Combine like terms: -200 + 200 = 0 0 + x = 100 + 200 x = 100 + 200 Combine like terms: 100 + 200 = 300 x = 300 Simplifying x = 300Subproblem 2
x + -200 = -100 Simplifying x + -200 = -100 Reorder the terms: -200 + x = -100 Solving -200 + x = -100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -100 + 200 Combine like terms: -200 + 200 = 0 0 + x = -100 + 200 x = -100 + 200 Combine like terms: -100 + 200 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {300, 100}
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