Question

How do you solve this using quadtratic formula? (7x-2)^2=4

Answer 1

See method to obtain equation in form `ax^2+bx+c=0`

Explanation:

First expand out the brackets:
`(7x-2)^2 = (7x-2)*(7x-2)=49x^2-28x+4`

in the original equation, we had a 4 on the right hand side, and we need a zero to apply the quadratic formula, so we subtract 4 from both sides, giving:

`49x^2-28x+4-4=4-4`
`=>49x^2-28x=0`
a factor of 7 can be taken out to leave:
`=> 7x^2 -4x=0`

Then the quadratic formula can be applied where `a=7, b=-4 and c=0`

`x=(-b±sqrt(b^2-4ac))/(2a)`

You can also solve easily without quadratic formula:
Factorise:
`x(7x-4)=0`

Two solutions:
`x=0` and `7x-4=0`

The latter leads to `x= 4/7`