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Simplifying 2x2 + 2x + -459 = 0 Reorder the terms: -459 + 2x + 2x2 = 0 Solving -459 + 2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -229.5 + x + x2 = 0 Move the constant term to the right: Add '229.5' to each side of the equation. -229.5 + x + 229.5 + x2 = 0 + 229.5 Reorder the terms: -229.5 + 229.5 + x + x2 = 0 + 229.5 Combine like terms: -229.5 + 229.5 = 0.0 0.0 + x + x2 = 0 + 229.5 x + x2 = 0 + 229.5 Combine like terms: 0 + 229.5 = 229.5 x + x2 = 229.5 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 = 229.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 229.5 + 0.25 Combine like terms: 229.5 + 0.25 = 229.75 1.25 + x2 = 229.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 229.75 Calculate the square root of the right side: 15.157506391 Break this problem into two subproblems by setting (x + 0.5) equal to 15.157506391 and -15.157506391.Subproblem 1
x + 0.5 = 15.157506391 Simplifying x + 0.5 = 15.157506391 Reorder the terms: 0.5 + x = 15.157506391 Solving 0.5 + x = 15.157506391 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 = 15.157506391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.157506391 + -0.5 x = 15.157506391 + -0.5 Combine like terms: 15.157506391 + -0.5 = 14.657506391 x = 14.657506391 Simplifying x = 14.657506391Subproblem 2
x + 0.5 = -15.157506391 Simplifying x + 0.5 = -15.157506391 Reorder the terms: 0.5 + x = -15.157506391 Solving 0.5 + x = -15.157506391 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 = -15.157506391 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.157506391 + -0.5 x = -15.157506391 + -0.5 Combine like terms: -15.157506391 + -0.5 = -15.657506391 x = -15.657506391 Simplifying x = -15.657506391Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.657506391, -15.657506391}
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