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

1 Answer
Mar 8, 2018

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#