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Simplifying 0.02x2 + -10x + 200 = 0 Reorder the terms: 200 + -10x + 0.02x2 = 0 Solving 200 + -10x + 0.02x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 10000 + -500x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + -500x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + -500x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + -500x + x2 = 0 + -10000 -500x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 -500x + x2 = -10000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -10000 + 62500 Reorder the terms: 62500 + -500x + x2 = -10000 + 62500 Combine like terms: -10000 + 62500 = 52500 62500 + -500x + x2 = 52500 Factor a perfect square on the left side: (x + -250)(x + -250) = 52500 Calculate the square root of the right side: 229.128784748 Break this problem into two subproblems by setting (x + -250) equal to 229.128784748 and -229.128784748.Subproblem 1
x + -250 = 229.128784748 Simplifying x + -250 = 229.128784748 Reorder the terms: -250 + x = 229.128784748 Solving -250 + x = 229.128784748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = 229.128784748 + 250 Combine like terms: -250 + 250 = 0 0 + x = 229.128784748 + 250 x = 229.128784748 + 250 Combine like terms: 229.128784748 + 250 = 479.128784748 x = 479.128784748 Simplifying x = 479.128784748Subproblem 2
x + -250 = -229.128784748 Simplifying x + -250 = -229.128784748 Reorder the terms: -250 + x = -229.128784748 Solving -250 + x = -229.128784748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + x = -229.128784748 + 250 Combine like terms: -250 + 250 = 0 0 + x = -229.128784748 + 250 x = -229.128784748 + 250 Combine like terms: -229.128784748 + 250 = 20.871215252 x = 20.871215252 Simplifying x = 20.871215252Solution
The solution to the problem is based on the solutions from the subproblems. x = {479.128784748, 20.871215252}
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