Answer:
• (7x-1)(x-3)=0
,
• x=1/7 or 3
Explanation:
Given the quadratic equation:
[tex]7x^2-22x+3=0[/tex]
First, multiply the first and the last term:
[tex]7x^2\times3=21x^2[/tex]
Next, find factors of the product above that add up to the middle term:
[tex]-21x-x=-22x[/tex]
Therefore, we obtain the factored form below:
[tex]\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}[/tex]
The equation in factored form is:
[tex](7x-1)(x^{}-3)=0[/tex]
Next, solve for x:
[tex]\begin{gathered} 7x-1=0\lor x-3=0 \\ 7x=1\lor x=3 \\ x=\frac{1}{7}\text{ or }x=3 \end{gathered}[/tex]
The solution to the equation is x=1/7 or 3.
