Write the the function $\displaystyle {f{{\left({x}\right)}}}=-{2}{x}^{{2}}-{16}{x}+{35}$ in the form $\displaystyle {f{{\left({x}\right)}}}={a}{\left({x}-{p}\right)}^{{2}}+{q}$ by completing the square:

1. We take out the coefficient of $\displaystyle {x}^{{2}},$ $\displaystyle {a},$ as a factor from the first two terms:

$\displaystyle {f{{\left({x}\right)}}}=$$\displaystyle {\left({x}^{{2}}+\right.}$ $\displaystyle {x}{)}+{35}$

2. Then we add half of the coefficient of $\displaystyle {x}$ squared, $\displaystyle {\left(\frac{{b}}{{2}}\right)}^{{2}}$, inside the bracket and subtract it outside $\displaystyle {a}$ times, $\displaystyle {a}{\left(\frac{{b}}{{2}}\right)}^{{2}}$.

$\displaystyle {f{{\left({x}\right)}}}=$$\displaystyle {\left({x}^{{2}}+\right.}$$\displaystyle {x}+$$\displaystyle {)}+{35}-$

3. Then we factorize the bracket and simplify outside the bracket.

$\displaystyle {f{{\left({x}\right)}}}=$$\displaystyle {\left({x}+\right.}$$\displaystyle {)}^{{2}}+$