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Simplifying x2 + -11x + -69 = 0 Reorder the terms: -69 + -11x + x2 = 0 Solving -69 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + -11x + 69 + x2 = 0 + 69 Reorder the terms: -69 + 69 + -11x + x2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + -11x + x2 = 0 + 69 -11x + x2 = 0 + 69 Combine like terms: 0 + 69 = 69 -11x + x2 = 69 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 = 69 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 69 + 30.25 Combine like terms: 69 + 30.25 = 99.25 30.25 + -11x + x2 = 99.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (x + -5.5) equal to 9.962429423 and -9.962429423.Subproblem 1
x + -5.5 = 9.962429423 Simplifying x + -5.5 = 9.962429423 Reorder the terms: -5.5 + x = 9.962429423 Solving -5.5 + x = 9.962429423 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 = 9.962429423 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 9.962429423 + 5.5 x = 9.962429423 + 5.5 Combine like terms: 9.962429423 + 5.5 = 15.462429423 x = 15.462429423 Simplifying x = 15.462429423Subproblem 2
x + -5.5 = -9.962429423 Simplifying x + -5.5 = -9.962429423 Reorder the terms: -5.5 + x = -9.962429423 Solving -5.5 + x = -9.962429423 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 = -9.962429423 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -9.962429423 + 5.5 x = -9.962429423 + 5.5 Combine like terms: -9.962429423 + 5.5 = -4.462429423 x = -4.462429423 Simplifying x = -4.462429423Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.462429423, -4.462429423}
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