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Simplifying x2 + -11x + 19 = 5 + -5 Reorder the terms: 19 + -11x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 19 + -11x + x2 = 0 Solving 19 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + -11x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -11x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -11x + x2 = 0 + -19 -11x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -11x + x2 = -19 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 = -19 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -19 + 30.25 Combine like terms: -19 + 30.25 = 11.25 30.25 + -11x + x2 = 11.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + -5.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + -5.5 = 3.354101966 Simplifying x + -5.5 = 3.354101966 Reorder the terms: -5.5 + x = 3.354101966 Solving -5.5 + x = 3.354101966 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 = 3.354101966 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.354101966 + 5.5 x = 3.354101966 + 5.5 Combine like terms: 3.354101966 + 5.5 = 8.854101966 x = 8.854101966 Simplifying x = 8.854101966Subproblem 2
x + -5.5 = -3.354101966 Simplifying x + -5.5 = -3.354101966 Reorder the terms: -5.5 + x = -3.354101966 Solving -5.5 + x = -3.354101966 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 = -3.354101966 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.354101966 + 5.5 x = -3.354101966 + 5.5 Combine like terms: -3.354101966 + 5.5 = 2.145898034 x = 2.145898034 Simplifying x = 2.145898034Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.854101966, 2.145898034}
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