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Simplifying x2 + -11x + -17 = 0 Reorder the terms: -17 + -11x + x2 = 0 Solving -17 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -11x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -11x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -11x + x2 = 0 + 17 -11x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -11x + x2 = 17 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 = 17 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 17 + 30.25 Combine like terms: 17 + 30.25 = 47.25 30.25 + -11x + x2 = 47.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + -5.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + -5.5 = 6.873863542 Simplifying x + -5.5 = 6.873863542 Reorder the terms: -5.5 + x = 6.873863542 Solving -5.5 + x = 6.873863542 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 = 6.873863542 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.873863542 + 5.5 x = 6.873863542 + 5.5 Combine like terms: 6.873863542 + 5.5 = 12.373863542 x = 12.373863542 Simplifying x = 12.373863542Subproblem 2
x + -5.5 = -6.873863542 Simplifying x + -5.5 = -6.873863542 Reorder the terms: -5.5 + x = -6.873863542 Solving -5.5 + x = -6.873863542 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 = -6.873863542 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.873863542 + 5.5 x = -6.873863542 + 5.5 Combine like terms: -6.873863542 + 5.5 = -1.373863542 x = -1.373863542 Simplifying x = -1.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.373863542, -1.373863542}
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