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Simplifying 2x2 + 11x + -26 = 0 Reorder the terms: -26 + 11x + 2x2 = 0 Solving -26 + 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'. -13 + 5.5x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 5.5x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 5.5x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 5.5x + x2 = 0 + 13 5.5x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 5.5x + x2 = 13 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 = 13 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 13 + 7.5625 Combine like terms: 13 + 7.5625 = 20.5625 7.5625 + 5.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + 2.75) equal to 4.534589287 and -4.534589287.Subproblem 1
x + 2.75 = 4.534589287 Simplifying x + 2.75 = 4.534589287 Reorder the terms: 2.75 + x = 4.534589287 Solving 2.75 + x = 4.534589287 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 = 4.534589287 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 4.534589287 + -2.75 x = 4.534589287 + -2.75 Combine like terms: 4.534589287 + -2.75 = 1.784589287 x = 1.784589287 Simplifying x = 1.784589287Subproblem 2
x + 2.75 = -4.534589287 Simplifying x + 2.75 = -4.534589287 Reorder the terms: 2.75 + x = -4.534589287 Solving 2.75 + x = -4.534589287 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 = -4.534589287 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -4.534589287 + -2.75 x = -4.534589287 + -2.75 Combine like terms: -4.534589287 + -2.75 = -7.284589287 x = -7.284589287 Simplifying x = -7.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.784589287, -7.284589287}
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