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Solve for $c$ in $(c - 7)^2 = 81 + 5c$.

 Dec 13, 2023
 #1
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We can solve for c in the equation (c−7)2=81+5c by following these steps:

 

Expand the square on the left side: (c - 7)^2 = c^2 - 14c + 49

 

Combine like terms on the right side: c^2 - 14c + 49 = 81 + 5c

 

Move all c terms to one side and move the constant term to the other side: c^2 - 14c - 5c = 81 - 49

 

Combine like terms: c^2 - 19c = 32

 

Factor the equation: (c - 8)(c - 4) = 0

 

Solve for c using the zero product property: c = 8 or c = 4

 

Therefore, the possible solutions for c are 4​ and 8​.

 Dec 13, 2023

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