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Simplifying 2x2 + -11x + -43 = 0 Reorder the terms: -43 + -11x + 2x2 = 0 Solving -43 + -11x + 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'. -21.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + -5.5x + 21.5 + x2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + -5.5x + x2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + -5.5x + x2 = 0 + 21.5 -5.5x + x2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 -5.5x + x2 = 21.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 21.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 21.5 + 7.5625 Combine like terms: 21.5 + 7.5625 = 29.0625 7.5625 + -5.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + -2.75) equal to 5.390964663 and -5.390964663.Subproblem 1
x + -2.75 = 5.390964663 Simplifying x + -2.75 = 5.390964663 Reorder the terms: -2.75 + x = 5.390964663 Solving -2.75 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 5.390964663 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 5.390964663 + 2.75 x = 5.390964663 + 2.75 Combine like terms: 5.390964663 + 2.75 = 8.140964663 x = 8.140964663 Simplifying x = 8.140964663Subproblem 2
x + -2.75 = -5.390964663 Simplifying x + -2.75 = -5.390964663 Reorder the terms: -2.75 + x = -5.390964663 Solving -2.75 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -5.390964663 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -5.390964663 + 2.75 x = -5.390964663 + 2.75 Combine like terms: -5.390964663 + 2.75 = -2.640964663 x = -2.640964663 Simplifying x = -2.640964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.140964663, -2.640964663}
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