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Simplifying (c + 3)(c + 3) = 25 Reorder the terms: (3 + c)(c + 3) = 25 Reorder the terms: (3 + c)(3 + c) = 25 Multiply (3 + c) * (3 + c) (3(3 + c) + c(3 + c)) = 25 ((3 * 3 + c * 3) + c(3 + c)) = 25 ((9 + 3c) + c(3 + c)) = 25 (9 + 3c + (3 * c + c * c)) = 25 (9 + 3c + (3c + c2)) = 25 Combine like terms: 3c + 3c = 6c (9 + 6c + c2) = 25 Solving 9 + 6c + c2 = 25 Solving for variable 'c'. Reorder the terms: 9 + -25 + 6c + c2 = 25 + -25 Combine like terms: 9 + -25 = -16 -16 + 6c + c2 = 25 + -25 Combine like terms: 25 + -25 = 0 -16 + 6c + c2 = 0 Factor a trinomial. (-8 + -1c)(2 + -1c) = 0Subproblem 1
Set the factor '(-8 + -1c)' equal to zero and attempt to solve: Simplifying -8 + -1c = 0 Solving -8 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1c = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1c = 0 + 8 -1c = 0 + 8 Combine like terms: 0 + 8 = 8 -1c = 8 Divide each side by '-1'. c = -8 Simplifying c = -8Subproblem 2
Set the factor '(2 + -1c)' equal to zero and attempt to solve: Simplifying 2 + -1c = 0 Solving 2 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1c = 0 + -2 -1c = 0 + -2 Combine like terms: 0 + -2 = -2 -1c = -2 Divide each side by '-1'. c = 2 Simplifying c = 2Solution
c = {-8, 2}
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