Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0

Question

2
𝑥
2
−
14
𝑥
=
0
.(1 point)
The smaller solution is x=
𝑥
=
, and the larger solution is x=
𝑥
=

Answer 1

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. The GCF of \( 2x^2 \) and \( -14x \) is \( 2x \).

Now we can factor out \( 2x \) from the equation:

\[ 2x(x - 7) = 0 \]

Next, we set each factor equal to zero:

1. \( 2x = 0 \)
2. \( x - 7 = 0 \)

From \( 2x = 0 \):

\[ x = 0 \]

From \( x - 7 = 0 \):

\[ x = 7 \]

Thus, the solutions to the equation are \( x = 0 \) and \( x = 7 \).

The smaller solution is \( x = 0 \) and the larger solution is \( x = 7 \).