# How do you solve #f(x)=2x^2-12x+17# by completing the square?

##### 2 Answers

#### Answer:

#### Explanation:

so,

Hence,

By 'solving' I assume you mean

i.e.

so,

:)>

#### Answer:

#### Explanation:

To

#color(blue)"complete the square"# add

#(1/2" coefficient of x-term")^2# Require coefficient of

#x^2# term to be 1

#f(x)=2(x^2-6x)+17#

#color(white)(f(x))=2(x^2-6xcolor(red)(+9 -9))+17# Since we have added +9 which is not there we must also subtract 9

#f(x)=2(x-3)^2-18+17#

#rArrf(x)=2(x-3)^2-1# To solve

#color(blue)"equate f(x) to zero"#

#rArr2(x-3)^2-1=0#

#rArr2(x-3)^2=1#

#rArr(x-3)^2=1/2#

#color(blue)"take the square root of both sides"#

#sqrt((x-3)^2)=+-sqrt(1/2)#

#rArrx-3=+-1/sqrt2#

#rArrx=3+-1/sqrt2=3+-sqrt2/2larrcolor(red)" rationalise denominator"#