Solve the following quadratic equation by factoring out the greatest common factor

Question

$(GCF)$
$2x^{2}-14x=0$
(1 point)
The smaller solution is $x=$ and the larger solution is $x=$

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 in the equation.

The GCF of \(2x^2\) and \(-14x\) is \(2x\). We can factor \(2x\) out from the equation:

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

Next, we set each factor equal to zero to find the solutions:

1. Setting the first factor equal to zero: \[ 2x = 0 \implies x = 0 \]

2. Setting the second factor equal to zero: \[ x - 7 = 0 \implies x = 7 \]

Thus, the solutions to the equation are:

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

In summary, the answers are:

• The smaller solution is \(x = 0\)
• The larger solution is \(x = 7\)