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Simplifying c2 + 5c + 4c = -5 Reorder the terms: 5c + 4c + c2 = -5 Combine like terms: 5c + 4c = 9c 9c + c2 = -5 Solving 9c + c2 = -5 Solving for variable 'c'. Reorder the terms: 5 + 9c + c2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 9c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 9c + -5 + c2 = 0 + -5 Reorder the terms: 5 + -5 + 9c + c2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9c + c2 = 0 + -5 9c + c2 = 0 + -5 Combine like terms: 0 + -5 = -5 9c + c2 = -5 The c term is 9c. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9c + 20.25 + c2 = -5 + 20.25 Reorder the terms: 20.25 + 9c + c2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + 9c + c2 = 15.25 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (c + 4.5) equal to 3.905124838 and -3.905124838.Subproblem 1
c + 4.5 = 3.905124838 Simplifying c + 4.5 = 3.905124838 Reorder the terms: 4.5 + c = 3.905124838 Solving 4.5 + c = 3.905124838 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = 3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 3.905124838 + -4.5 c = 3.905124838 + -4.5 Combine like terms: 3.905124838 + -4.5 = -0.594875162 c = -0.594875162 Simplifying c = -0.594875162Subproblem 2
c + 4.5 = -3.905124838 Simplifying c + 4.5 = -3.905124838 Reorder the terms: 4.5 + c = -3.905124838 Solving 4.5 + c = -3.905124838 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + c = -3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -3.905124838 + -4.5 c = -3.905124838 + -4.5 Combine like terms: -3.905124838 + -4.5 = -8.405124838 c = -8.405124838 Simplifying c = -8.405124838Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.594875162, -8.405124838}
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