Question

Complete the square for the expressions:
i)2x^2-5x
ii)3x^2+9x
iii)3x^2-x

Answer 1

i) start with
\[2(x^2-\frac{5}{2}x)\] then think "half of 5/2 is 5/4" and
\[(\frac{5}{4})^2=\frac{25}{16}\] so you complete the square via
\[2(x^2-\frac{5}{2}x+\frac{25}{16})=2(x-\frac{5}{4})^2\]

Answer 2

3(x^2+3x+9/4)=3(x+3/2)^2