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Simplifying c2 + 11c + 16 = 0 Reorder the terms: 16 + 11c + c2 = 0 Solving 16 + 11c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 11c + -16 + c2 = 0 + -16 Reorder the terms: 16 + -16 + 11c + c2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 11c + c2 = 0 + -16 11c + c2 = 0 + -16 Combine like terms: 0 + -16 = -16 11c + c2 = -16 The c term is 11c. 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. 11c + 30.25 + c2 = -16 + 30.25 Reorder the terms: 30.25 + 11c + c2 = -16 + 30.25 Combine like terms: -16 + 30.25 = 14.25 30.25 + 11c + c2 = 14.25 Factor a perfect square on the left side: (c + 5.5)(c + 5.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (c + 5.5) equal to 3.774917218 and -3.774917218.Subproblem 1
c + 5.5 = 3.774917218 Simplifying c + 5.5 = 3.774917218 Reorder the terms: 5.5 + c = 3.774917218 Solving 5.5 + c = 3.774917218 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = 3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = 3.774917218 + -5.5 c = 3.774917218 + -5.5 Combine like terms: 3.774917218 + -5.5 = -1.725082782 c = -1.725082782 Simplifying c = -1.725082782Subproblem 2
c + 5.5 = -3.774917218 Simplifying c + 5.5 = -3.774917218 Reorder the terms: 5.5 + c = -3.774917218 Solving 5.5 + c = -3.774917218 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + c = -3.774917218 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = -3.774917218 + -5.5 c = -3.774917218 + -5.5 Combine like terms: -3.774917218 + -5.5 = -9.274917218 c = -9.274917218 Simplifying c = -9.274917218Solution
The solution to the problem is based on the solutions from the subproblems. c = {-1.725082782, -9.274917218}
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