To factor out the greatest common factor (GCF) and solve the quadratic equation \(7x = 56x\), we first rearrange the equation into standard form:
-
Rearranging the Equation:
Move all terms to one side of the equation:
\[ 7x - 56x = 0 \]
\[ -49x = 0 \] -
Factoring Out the GCF:
The GCF of \(7x\) and \(56x\) is \(7x\). We can factor as follows:
\[ 7x(1 - 8) = 0 \]
Here, we factored out \(7x\), but notice that this situation is a little different, as \(56x\) was derived from \(8 \times 7x\). -
Setting Factors to Zero:
Set the remaining factors to zero. We have:
\[ 7x = 0 \]
or
\[ (1 - 8) = 0 \] (since that factor makes no sense, we ignore it). -
Solving for x:
From \(7x = 0\), divide both sides by 7:
\[ x = 0 \]
The solution to the equation \(7x = 56x\) after factoring out the GCF is \(x = 0\).
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