Question:

Write $\displaystyle x^2 + 10x + 38$ in the form $\displaystyle (x+b)^2+c$ where the values of b and c are to be found.

(a) State the minimum value of $\displaystyle x^2 + 10x + 38$ and the value of $\displaystyle x$ for which this occurs.

(b) Determine the values of $\displaystyle x$ for which $\displaystyle x^2 + 10x + 38 \geq 22$.

Attempt:

$\displaystyle x^2 + 10x + 38$

$\displaystyle = (x + \frac{10}{2})^2 - (\frac{10}{2})^2 + 38$

$\displaystyle = (x + 5)^2 - 25 + 38$

What to do next?

$\displaystyle = (x + 5)^2 + 13$