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Simplifying 2x2 + -18x + -269 = 0 Reorder the terms: -269 + -18x + 2x2 = 0 Solving -269 + -18x + 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'. -134.5 + -9x + x2 = 0 Move the constant term to the right: Add '134.5' to each side of the equation. -134.5 + -9x + 134.5 + x2 = 0 + 134.5 Reorder the terms: -134.5 + 134.5 + -9x + x2 = 0 + 134.5 Combine like terms: -134.5 + 134.5 = 0.0 0.0 + -9x + x2 = 0 + 134.5 -9x + x2 = 0 + 134.5 Combine like terms: 0 + 134.5 = 134.5 -9x + x2 = 134.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 134.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 134.5 + 20.25 Combine like terms: 134.5 + 20.25 = 154.75 20.25 + -9x + x2 = 154.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 154.75 Calculate the square root of the right side: 12.439855305 Break this problem into two subproblems by setting (x + -4.5) equal to 12.439855305 and -12.439855305.Subproblem 1
x + -4.5 = 12.439855305 Simplifying x + -4.5 = 12.439855305 Reorder the terms: -4.5 + x = 12.439855305 Solving -4.5 + x = 12.439855305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 12.439855305 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 12.439855305 + 4.5 x = 12.439855305 + 4.5 Combine like terms: 12.439855305 + 4.5 = 16.939855305 x = 16.939855305 Simplifying x = 16.939855305Subproblem 2
x + -4.5 = -12.439855305 Simplifying x + -4.5 = -12.439855305 Reorder the terms: -4.5 + x = -12.439855305 Solving -4.5 + x = -12.439855305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -12.439855305 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -12.439855305 + 4.5 x = -12.439855305 + 4.5 Combine like terms: -12.439855305 + 4.5 = -7.939855305 x = -7.939855305 Simplifying x = -7.939855305Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.939855305, -7.939855305}
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