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Simplifying c2 + 8c + -44 = 0 Reorder the terms: -44 + 8c + c2 = 0 Solving -44 + 8c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 8c + 44 + c2 = 0 + 44 Reorder the terms: -44 + 44 + 8c + c2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 8c + c2 = 0 + 44 8c + c2 = 0 + 44 Combine like terms: 0 + 44 = 44 8c + c2 = 44 The c term is 8c. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8c + 16 + c2 = 44 + 16 Reorder the terms: 16 + 8c + c2 = 44 + 16 Combine like terms: 44 + 16 = 60 16 + 8c + c2 = 60 Factor a perfect square on the left side: (c + 4)(c + 4) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (c + 4) equal to 7.745966692 and -7.745966692.Subproblem 1
c + 4 = 7.745966692 Simplifying c + 4 = 7.745966692 Reorder the terms: 4 + c = 7.745966692 Solving 4 + c = 7.745966692 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = 7.745966692 + -4 Combine like terms: 4 + -4 = 0 0 + c = 7.745966692 + -4 c = 7.745966692 + -4 Combine like terms: 7.745966692 + -4 = 3.745966692 c = 3.745966692 Simplifying c = 3.745966692Subproblem 2
c + 4 = -7.745966692 Simplifying c + 4 = -7.745966692 Reorder the terms: 4 + c = -7.745966692 Solving 4 + c = -7.745966692 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + c = -7.745966692 + -4 Combine like terms: 4 + -4 = 0 0 + c = -7.745966692 + -4 c = -7.745966692 + -4 Combine like terms: -7.745966692 + -4 = -11.745966692 c = -11.745966692 Simplifying c = -11.745966692Solution
The solution to the problem is based on the solutions from the subproblems. c = {3.745966692, -11.745966692}
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