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Simplifying c2 + 9c + -8 = 0 Reorder the terms: -8 + 9c + c2 = 0 Solving -8 + 9c + c2 = 0 Solving for variable 'c'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 9c + 8 + c2 = 0 + 8 Reorder the terms: -8 + 8 + 9c + c2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9c + c2 = 0 + 8 9c + c2 = 0 + 8 Combine like terms: 0 + 8 = 8 9c + c2 = 8 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 = 8 + 20.25 Reorder the terms: 20.25 + 9c + c2 = 8 + 20.25 Combine like terms: 8 + 20.25 = 28.25 20.25 + 9c + c2 = 28.25 Factor a perfect square on the left side: (c + 4.5)(c + 4.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (c + 4.5) equal to 5.315072906 and -5.315072906.Subproblem 1
c + 4.5 = 5.315072906 Simplifying c + 4.5 = 5.315072906 Reorder the terms: 4.5 + c = 5.315072906 Solving 4.5 + c = 5.315072906 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 = 5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = 5.315072906 + -4.5 c = 5.315072906 + -4.5 Combine like terms: 5.315072906 + -4.5 = 0.815072906 c = 0.815072906 Simplifying c = 0.815072906Subproblem 2
c + 4.5 = -5.315072906 Simplifying c + 4.5 = -5.315072906 Reorder the terms: 4.5 + c = -5.315072906 Solving 4.5 + c = -5.315072906 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 = -5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + c = -5.315072906 + -4.5 c = -5.315072906 + -4.5 Combine like terms: -5.315072906 + -4.5 = -9.815072906 c = -9.815072906 Simplifying c = -9.815072906Solution
The solution to the problem is based on the solutions from the subproblems. c = {0.815072906, -9.815072906}
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