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Simplifying x2 + -11x + -26 = 9 Reorder the terms: -26 + -11x + x2 = 9 Solving -26 + -11x + x2 = 9 Solving for variable 'x'. Reorder the terms: -26 + -9 + -11x + x2 = 9 + -9 Combine like terms: -26 + -9 = -35 -35 + -11x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -35 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -11x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -11x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -11x + x2 = 0 + 35 -11x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -11x + x2 = 35 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 35 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 35 + 30.25 Combine like terms: 35 + 30.25 = 65.25 30.25 + -11x + x2 = 65.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + -5.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + -5.5 = 8.077747211 Simplifying x + -5.5 = 8.077747211 Reorder the terms: -5.5 + x = 8.077747211 Solving -5.5 + x = 8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 8.077747211 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 8.077747211 + 5.5 x = 8.077747211 + 5.5 Combine like terms: 8.077747211 + 5.5 = 13.577747211 x = 13.577747211 Simplifying x = 13.577747211Subproblem 2
x + -5.5 = -8.077747211 Simplifying x + -5.5 = -8.077747211 Reorder the terms: -5.5 + x = -8.077747211 Solving -5.5 + x = -8.077747211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -8.077747211 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -8.077747211 + 5.5 x = -8.077747211 + 5.5 Combine like terms: -8.077747211 + 5.5 = -2.577747211 x = -2.577747211 Simplifying x = -2.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.577747211, -2.577747211}
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