$x^{2} + 3 x + 3 x = x {}^{2}+ 6 x$

$x {}^{2}+ 6 x = 7$
$x {}^{2}+ 6 x - 7 = 0$
$(x - 1) (x + 7) = 0$
$x = 1$ of $x = ‐ 7$
Dus $x = 1$ , want $x$ kan niet negatief zijn.

$x {}^{2}+ 6 x = 16$
$x {}^{2}+ 6 x - 16 = 0$
$(x - 2) (x + 8) = 0$
$x = 2$ of $x = ‐ 8$
Dus $x = 2$ , want $x$ kan niet negatief zijn.

${(‐ 3 + \sqrt{19})}^{2} + 6 (‐ 3 + \sqrt{19}) = 9 - 6 \sqrt{19} + 19 - 18 + 6 \sqrt{19} = 10$ , klopt.

zijde = $x + 3$ ; oppervlakte = ${(x + 3)}^{2}$

$x^{2} + 6 x = {(x + 3)}^{2} - 9$

$x^{2} + 6 x = 11$
${(x + 3)}^{2} - 9 = 11$
${(x + 3)}^{2} = 20$
$x + 3 = \sqrt{20}$ of $x + 3 = ‐ \sqrt{20}$
$x = ‐ 3 + 2 \sqrt{5}$ of $x = ‐ 3 - 2 \sqrt{5}$

$x + 5$

$x = ‐ 5 + \sqrt{5}$ of $x = ‐ 5 - \sqrt{5}$

${(x + 5)}^{2} = 37$

$x = ‐ 5 + \sqrt{37}$ of $x = ‐ 5 - \sqrt{37}$

$x^{2} + 12 x = {(x + 6)}^{2} - 36$

$x^{2} + 12 x = 4$
${(x + 6)}^{2} - 36 = 4$
${(x + 6)}^{2} = 40$
$x + 6 = \sqrt{40}$ of $x + 6 = ‐ \sqrt{40}$
$x = ‐ 6 + 2 \sqrt{10}$ of $x = ‐ 6 - 2 \sqrt{10}$

$x^{2} + 12 x + 4 = 0$
${(x + 6)}^{2} - 36 + 4 = 0$
${(x + 6)}^{2} = 32$
$x + 6 = \sqrt{32}$ of $x + 6 = ‐ \sqrt{32}$
$x = ‐ 6 + 4 \sqrt{2}$ of $x = ‐ 6 - 4 \sqrt{2}$

$x^{2} - 20 x = {(x - 10)}^{2} - 100$

$x^{2} - 7 x = {(x - 3 \frac{1}{2})}^{2} - 12 \frac{1}{4}$

$x^{2} - 8 x = {(x - 4)}^{2} - 16$

$x^{2} + 11 x = {(x + 5 \frac{1}{2})}^{2} - 30 \frac{1}{4}$

$x^{2} - 21 x = {(x - 10 \frac{1}{2})}^{2} - 110 \frac{1}{4}$

$x^{2} + x = {(x + \frac{1}{2})}^{2} - \frac{1}{4}$

$x^{2} - x = {(x - \frac{1}{2})}^{2} - \frac{1}{4}$