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Simplifying (c + 2)(c + 2) = 9 Reorder the terms: (2 + c)(c + 2) = 9 Reorder the terms: (2 + c)(2 + c) = 9 Multiply (2 + c) * (2 + c) (2(2 + c) + c(2 + c)) = 9 ((2 * 2 + c * 2) + c(2 + c)) = 9 ((4 + 2c) + c(2 + c)) = 9 (4 + 2c + (2 * c + c * c)) = 9 (4 + 2c + (2c + c2)) = 9 Combine like terms: 2c + 2c = 4c (4 + 4c + c2) = 9 Solving 4 + 4c + c2 = 9 Solving for variable 'c'. Reorder the terms: 4 + -9 + 4c + c2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + 4c + c2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + 4c + c2 = 0 Factor a trinomial. (-5 + -1c)(1 + -1c) = 0Subproblem 1
Set the factor '(-5 + -1c)' equal to zero and attempt to solve: Simplifying -5 + -1c = 0 Solving -5 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1c = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1c = 0 + 5 -1c = 0 + 5 Combine like terms: 0 + 5 = 5 -1c = 5 Divide each side by '-1'. c = -5 Simplifying c = -5Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve: Simplifying 1 + -1c = 0 Solving 1 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1c = 0 + -1 -1c = 0 + -1 Combine like terms: 0 + -1 = -1 -1c = -1 Divide each side by '-1'. c = 1 Simplifying c = 1Solution
c = {-5, 1}
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