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Simplifying x2 + -11x + 16 = 0 Reorder the terms: 16 + -11x + x2 = 0 Solving 16 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -11x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -11x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -11x + x2 = 0 + -16 -11x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -11x + x2 = -16 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 = -16 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -16 + 30.25 Combine like terms: -16 + 30.25 = 14.25 30.25 + -11x + x2 = 14.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -5.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -5.5 = 3.774917218 Simplifying x + -5.5 = 3.774917218 Reorder the terms: -5.5 + x = 3.774917218 Solving -5.5 + x = 3.774917218 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 = 3.774917218 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.774917218 + 5.5 x = 3.774917218 + 5.5 Combine like terms: 3.774917218 + 5.5 = 9.274917218 x = 9.274917218 Simplifying x = 9.274917218Subproblem 2
x + -5.5 = -3.774917218 Simplifying x + -5.5 = -3.774917218 Reorder the terms: -5.5 + x = -3.774917218 Solving -5.5 + x = -3.774917218 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 = -3.774917218 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.774917218 + 5.5 x = -3.774917218 + 5.5 Combine like terms: -3.774917218 + 5.5 = 1.725082782 x = 1.725082782 Simplifying x = 1.725082782Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.274917218, 1.725082782}
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