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Simplifying 0.1x2 + -49x + 525 = 0 Reorder the terms: 525 + -49x + 0.1x2 = 0 Solving 525 + -49x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 5250 + -490x + x2 = 0 Move the constant term to the right: Add '-5250' to each side of the equation. 5250 + -490x + -5250 + x2 = 0 + -5250 Reorder the terms: 5250 + -5250 + -490x + x2 = 0 + -5250 Combine like terms: 5250 + -5250 = 0 0 + -490x + x2 = 0 + -5250 -490x + x2 = 0 + -5250 Combine like terms: 0 + -5250 = -5250 -490x + x2 = -5250 The x term is -490x. Take half its coefficient (-245). Square it (60025) and add it to both sides. Add '60025' to each side of the equation. -490x + 60025 + x2 = -5250 + 60025 Reorder the terms: 60025 + -490x + x2 = -5250 + 60025 Combine like terms: -5250 + 60025 = 54775 60025 + -490x + x2 = 54775 Factor a perfect square on the left side: (x + -245)(x + -245) = 54775 Calculate the square root of the right side: 234.040594769 Break this problem into two subproblems by setting (x + -245) equal to 234.040594769 and -234.040594769.Subproblem 1
x + -245 = 234.040594769 Simplifying x + -245 = 234.040594769 Reorder the terms: -245 + x = 234.040594769 Solving -245 + x = 234.040594769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + x = 234.040594769 + 245 Combine like terms: -245 + 245 = 0 0 + x = 234.040594769 + 245 x = 234.040594769 + 245 Combine like terms: 234.040594769 + 245 = 479.040594769 x = 479.040594769 Simplifying x = 479.040594769Subproblem 2
x + -245 = -234.040594769 Simplifying x + -245 = -234.040594769 Reorder the terms: -245 + x = -234.040594769 Solving -245 + x = -234.040594769 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '245' to each side of the equation. -245 + 245 + x = -234.040594769 + 245 Combine like terms: -245 + 245 = 0 0 + x = -234.040594769 + 245 x = -234.040594769 + 245 Combine like terms: -234.040594769 + 245 = 10.959405231 x = 10.959405231 Simplifying x = 10.959405231Solution
The solution to the problem is based on the solutions from the subproblems. x = {479.040594769, 10.959405231}
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