How do you solve x^2-14x+5=0 by completing the square?

1 Answer
Mar 21, 2018

x=7-2sqrt11 and x=7+2sqrt11

Explanation:

Half the second term of x put it in brackets and square it.

x^2-14x+5-> (x-7)^2+5

Take away the squared number of the number inside the bracket.

7^2=49 therefore -49

-> (x-7)^2-49+5

Simplify:

(x-7)^2-44

Solving:

Set equal to 0:

(x-7)^2-44=0

Add 44:

(x-7)^2=44

Square root:

x-7=pmsqrt44

Add 7:

x=7pmsqrt44

Simplifying:

sqrt44=sqrt4 xx sqrt11

sqrt4=2

sqrt11=sqrt11, It cannot be simplified as it is a prime number.

therefore x=7pmsqrt44 -> x=7pm2sqrt11

Therefore both answers are:

x=7-2sqrt11

and...

x=7+2sqrt11