1)) Is \( c=8 \) a solution to this equation? \( 0=(-8+c)^{2} \) yes yo no no no
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To determine if \( c=8 \) is a solution to the equation \( 0=(-8+c)^{2} \), substitute 8 in place of \( c \). This simplifies to \( 0=(-8+8)^{2} \), which further simplifies to \( 0=0^{2} \) or \( 0=0 \). Since this statement is true, yes, \( c=8 \) is indeed a solution! Now, let's consider the implications of this result. The equation \( 0=(-8+c)^{2} \) means that \( -8+c \) must equal 0, leading us to the conclusion that \( c \) must equal 8 for the equation to hold true. This showcases the concept of solving for variables with simple algebraic manipulation, reinforcing the importance of understanding equality in equations!