How do you solve #f(x)=2x^2-12x+17# by completing the square?
2 Answers
Explanation:
so,
Hence,
By 'solving' I assume you mean
i.e.
so,
:)>
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"#