Question

Factor the equation....

Answer 1

To factor the equation

`x^2-9x+14=0`

We will look for 2 numbers their product is 14, and their sum is 9

Since 14 = 2 x 7

Since 2 + 7 = 9

Then the factors will be (x - 2) and (x - 7)

`\begin{gathered} x^2-9x+14=0 \\ (x-2)(x-7)=0 \end{gathered}`

Equate each factor by 0 to find the values of x

`x-2=0`

Add 2 to both sides

`\begin{gathered} x-2+2=0+2 \\ x=2 \end{gathered}`
`x-7=0`

Add 7 to both sides

`\begin{gathered} x-7+7=0+7 \\ x=7 \end{gathered}`

The values of x are 2 and 7