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Simplifying x + 0.5x2 = 250 Solving x + 0.5x2 = 250 Solving for variable 'x'. Reorder the terms: -250 + x + 0.5x2 = 250 + -250 Combine like terms: 250 + -250 = 0 -250 + x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -500 + 2x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + 2x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + 2x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + 2x + x2 = 0 + 500 2x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 2x + x2 = 500 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 2x + 0.25 + x2 = 500 + 0.25 Reorder the terms: 0.25 + 2x + x2 = 500 + 0.25 Combine like terms: 500 + 0.25 = 500.25 0.25 + 2x + x2 = 500.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 500.25 Calculate the square root of the right side: 22.366269246 Break this problem into two subproblems by setting (x + 0.5) equal to 22.366269246 and -22.366269246.Subproblem 1
x + 0.5 = 22.366269246 Simplifying x + 0.5 = 22.366269246 Reorder the terms: 0.5 + x = 22.366269246 Solving 0.5 + x = 22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 22.366269246 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 22.366269246 + -0.5 x = 22.366269246 + -0.5 Combine like terms: 22.366269246 + -0.5 = 21.866269246 x = 21.866269246 Simplifying x = 21.866269246Subproblem 2
x + 0.5 = -22.366269246 Simplifying x + 0.5 = -22.366269246 Reorder the terms: 0.5 + x = -22.366269246 Solving 0.5 + x = -22.366269246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -22.366269246 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -22.366269246 + -0.5 x = -22.366269246 + -0.5 Combine like terms: -22.366269246 + -0.5 = -22.866269246 x = -22.866269246 Simplifying x = -22.866269246Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.866269246, -22.866269246}
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