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Simplifying 0.5x2 + 0.5x = 1275 Reorder the terms: 0.5x + 0.5x2 = 1275 Solving 0.5x + 0.5x2 = 1275 Solving for variable 'x'. Reorder the terms: -1275 + 0.5x + 0.5x2 = 1275 + -1275 Combine like terms: 1275 + -1275 = 0 -1275 + 0.5x + 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'. -2550 + x + x2 = 0 Move the constant term to the right: Add '2550' to each side of the equation. -2550 + x + 2550 + x2 = 0 + 2550 Reorder the terms: -2550 + 2550 + x + x2 = 0 + 2550 Combine like terms: -2550 + 2550 = 0 0 + x + x2 = 0 + 2550 x + x2 = 0 + 2550 Combine like terms: 0 + 2550 = 2550 x + x2 = 2550 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. + 0.25 + x2 = 2550 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 2550 + 0.25 Combine like terms: 2550 + 0.25 = 2550.25 1.25 + x2 = 2550.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2550.25 Calculate the square root of the right side: 50.5 Break this problem into two subproblems by setting (x + 0.5) equal to 50.5 and -50.5.Subproblem 1
x + 0.5 = 50.5 Simplifying x + 0.5 = 50.5 Reorder the terms: 0.5 + x = 50.5 Solving 0.5 + x = 50.5 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 = 50.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 50.5 + -0.5 x = 50.5 + -0.5 Combine like terms: 50.5 + -0.5 = 50 x = 50 Simplifying x = 50Subproblem 2
x + 0.5 = -50.5 Simplifying x + 0.5 = -50.5 Reorder the terms: 0.5 + x = -50.5 Solving 0.5 + x = -50.5 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 = -50.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -50.5 + -0.5 x = -50.5 + -0.5 Combine like terms: -50.5 + -0.5 = -51 x = -51 Simplifying x = -51Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -51}
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