Question

complete the square: $4x^2 5x 2$. enter your answer in the form $a(x u)^2 v$, where $a,$ $u,$ and $v$ are replaced by numbers.

Answer 1

I assume the missing symbols are plus signs, so we have

`4x^2 + 5x + 2 = 4\left(x^2 + \frac54x\right) + 2 \\\\ ~~~~~~~~ = 4 \left(x^2 + \frac54x + \left(\frac58\right)^2 - \left(\frac58\right)^2\right) + 2 \\\\ ~~~~~~~~ = 4 \left(x^2 + \frac54x + \left(\frac58\right)^2\right) - (25)/(16) + 2 \\\\ ~~~~~~~~ = \boxed{4 \left(x + \frac58\right)^2 + \frac7{16}}`

so that
`a=4`,
`u=\frac58` and
`v=\frac7{16}`.