To solve the quadratic equation \( 2x^2 - 14x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms in the equation.
-
The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \).
-
We factor out the GCF \( 2x \):
\[ 2x(x - 7) = 0 \]
-
Now we can set each factor equal to zero:
\[ 2x = 0 \quad \text{or} \quad x - 7 = 0 \]
-
Solving each equation gives:
-
From \( 2x = 0 \): \[ x = 0 \]
-
From \( x - 7 = 0 \): \[ x = 7 \]
-
-
Therefore, the solutions to the equation \( 2x^2 - 14x = 0 \) are:
\[ x = 0 \quad \text{and} \quad x = 7 \]
1 answer