Question

Rewrite each quadratic expressed in factored form. Then Solve the equation7x^2-22x+3=0

Answer 1

• (7x-1)(x-3)=0

,

• x=1/7 or 3

Step-by-step explanation:

Given the quadratic equation:

`7x^2-22x+3=0`

First, multiply the first and the last term:

`7x^2*3=21x^2`

Next, find factors of the product above that add up to the middle term:

`-21x-x=-22x`

Therefore, we obtain the factored form below:

`\begin{gathered} 7x^2-22x+3=0 \\ \implies7x^2-21x-x+3=0 \\ \implies7x(x^{}-3)-1(x-3)=0 \\ \implies(7x-1)(x^{}-3)=0 \end{gathered}`

The equation in factored form is:

`(7x-1)(x^{}-3)=0`

Next, solve for x:

`\begin{gathered} 7x-1=0\lor x-3=0 \\ 7x=1\lor x=3 \\ x=(1)/(7)\text{ or }x=3 \end{gathered}`

The solution to the equation is x=1/7 or 3.