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Simplifying 0.1x2 + 49x = 1500 Reorder the terms: 49x + 0.1x2 = 1500 Solving 49x + 0.1x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 49x + 0.1x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 49x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -15000 + 490x + x2 = 0 Move the constant term to the right: Add '15000' to each side of the equation. -15000 + 490x + 15000 + x2 = 0 + 15000 Reorder the terms: -15000 + 15000 + 490x + x2 = 0 + 15000 Combine like terms: -15000 + 15000 = 0 0 + 490x + x2 = 0 + 15000 490x + x2 = 0 + 15000 Combine like terms: 0 + 15000 = 15000 490x + x2 = 15000 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 = 15000 + 60025 Reorder the terms: 60025 + 490x + x2 = 15000 + 60025 Combine like terms: 15000 + 60025 = 75025 60025 + 490x + x2 = 75025 Factor a perfect square on the left side: (x + 245)(x + 245) = 75025 Calculate the square root of the right side: 273.906918496 Break this problem into two subproblems by setting (x + 245) equal to 273.906918496 and -273.906918496.Subproblem 1
x + 245 = 273.906918496 Simplifying x + 245 = 273.906918496 Reorder the terms: 245 + x = 273.906918496 Solving 245 + x = 273.906918496 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 = 273.906918496 + -245 Combine like terms: 245 + -245 = 0 0 + x = 273.906918496 + -245 x = 273.906918496 + -245 Combine like terms: 273.906918496 + -245 = 28.906918496 x = 28.906918496 Simplifying x = 28.906918496Subproblem 2
x + 245 = -273.906918496 Simplifying x + 245 = -273.906918496 Reorder the terms: 245 + x = -273.906918496 Solving 245 + x = -273.906918496 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 = -273.906918496 + -245 Combine like terms: 245 + -245 = 0 0 + x = -273.906918496 + -245 x = -273.906918496 + -245 Combine like terms: -273.906918496 + -245 = -518.906918496 x = -518.906918496 Simplifying x = -518.906918496Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.906918496, -518.906918496}
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