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Simplifying c2 + 11c + 18 = 9 Reorder the terms: 18 + 11c + c2 = 9 Solving 18 + 11c + c2 = 9 Solving for variable 'c'. Reorder the terms: 18 + -9 + 11c + c2 = 9 + -9 Combine like terms: 18 + -9 = 9 9 + 11c + c2 = 9 + -9 Combine like terms: 9 + -9 = 0 9 + 11c + c2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 11c + -9 + c2 = 0 + -9 Reorder the terms: 9 + -9 + 11c + c2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 11c + c2 = 0 + -9 11c + c2 = 0 + -9 Combine like terms: 0 + -9 = -9 11c + c2 = -9 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 = -9 + 30.25 Reorder the terms: 30.25 + 11c + c2 = -9 + 30.25 Combine like terms: -9 + 30.25 = 21.25 30.25 + 11c + c2 = 21.25 Factor a perfect square on the left side: (c + 5.5)(c + 5.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (c + 5.5) equal to 4.609772229 and -4.609772229.Subproblem 1
c + 5.5 = 4.609772229 Simplifying c + 5.5 = 4.609772229 Reorder the terms: 5.5 + c = 4.609772229 Solving 5.5 + c = 4.609772229 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 = 4.609772229 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = 4.609772229 + -5.5 c = 4.609772229 + -5.5 Combine like terms: 4.609772229 + -5.5 = -0.890227771 c = -0.890227771 Simplifying c = -0.890227771Subproblem 2
c + 5.5 = -4.609772229 Simplifying c + 5.5 = -4.609772229 Reorder the terms: 5.5 + c = -4.609772229 Solving 5.5 + c = -4.609772229 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 = -4.609772229 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + c = -4.609772229 + -5.5 c = -4.609772229 + -5.5 Combine like terms: -4.609772229 + -5.5 = -10.109772229 c = -10.109772229 Simplifying c = -10.109772229Solution
The solution to the problem is based on the solutions from the subproblems. c = {-0.890227771, -10.109772229}
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