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Simplifying c2 + -13c + 28 = 0 Reorder the terms: 28 + -13c + c2 = 0 Solving 28 + -13c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -13c + -28 + c2 = 0 + -28 Reorder the terms: 28 + -28 + -13c + c2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -13c + c2 = 0 + -28 -13c + c2 = 0 + -28 Combine like terms: 0 + -28 = -28 -13c + c2 = -28 The c term is -13c. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13c + 42.25 + c2 = -28 + 42.25 Reorder the terms: 42.25 + -13c + c2 = -28 + 42.25 Combine like terms: -28 + 42.25 = 14.25 42.25 + -13c + c2 = 14.25 Factor a perfect square on the left side: (c + -6.5)(c + -6.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (c + -6.5) equal to 3.774917218 and -3.774917218.Subproblem 1
c + -6.5 = 3.774917218 Simplifying c + -6.5 = 3.774917218 Reorder the terms: -6.5 + c = 3.774917218 Solving -6.5 + c = 3.774917218 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + c = 3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + c = 3.774917218 + 6.5 c = 3.774917218 + 6.5 Combine like terms: 3.774917218 + 6.5 = 10.274917218 c = 10.274917218 Simplifying c = 10.274917218Subproblem 2
c + -6.5 = -3.774917218 Simplifying c + -6.5 = -3.774917218 Reorder the terms: -6.5 + c = -3.774917218 Solving -6.5 + c = -3.774917218 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + c = -3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + c = -3.774917218 + 6.5 c = -3.774917218 + 6.5 Combine like terms: -3.774917218 + 6.5 = 2.725082782 c = 2.725082782 Simplifying c = 2.725082782Solution
The solution to the problem is based on the solutions from the subproblems. c = {10.274917218, 2.725082782}
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