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$2 x = 7$
$x = 3 \frac{1}{2}$

$2 x + 7 = 4 x + 1$
$7 = 2 x + 1$
$6 = 2 x$
$3 = x$

$x^{2} = 16$
$x = 4$ of $x = ‐ 4$

${(x + 6)}^{2} = 16$
$x + 6 = 4$ of $x + 6 = ‐ 4$
$x = ‐ 2$ of $x = ‐ 10$

$x^{2} = ‐ 16$
Er is geen oplossing, want het kwadraat van een getal kan niet negatief zijn.

$x^{2} = 7$
$x = \sqrt{7}$ of $x = ‐ \sqrt{7}$

${(x + 5)}^{2} = 7$
$x + 5 = \sqrt{7}$ of $x + 5 = ‐ \sqrt{7}$
$x = ‐ 5 + \sqrt{7}$ of $x = ‐ 5 - \sqrt{7}$

$x^{2} = x$
$x^{2} - x = 0$
$x (x - 1) = 0$
$x = 0$ of $x = 1$

$x^{2} = ‐ x$
$x^{2} + x = 0$
$x (x + 1) = 0$
$x = 0$ of $x = ‐ 1$

$x^{2} = 2 x$
$x^{2} - 2 x = 0$
$x (x - 2) = 0$
$x = 0$ of $x = 2$

$\frac{1}{x} = \frac{1}{7}$
$x = 7$

$\frac{1}{x + 1} = \frac{1}{7}$
$x + 1 = 7$
$x = 6$

$\frac{1}{x} = \frac{2}{7}$
$\frac{2}{2 x} = \frac{2}{7}$
$2 x = 7$
$x = 3 \frac{1}{2}$

$\frac{1}{x} = 7$
$x = \frac{1}{7}$

$\frac{2}{x} = 7$
$\frac{1}{x} = 3 \frac{1}{2}$
$x = \frac{1}{3 \frac{1}{2}} = \frac{2}{7}$

$\frac{2}{x} = \frac{4}{7}$
$\frac{4}{2 x} = \frac{4}{7}$
$2 x = 7$
$x = 3 \frac{1}{2}$

$\sqrt{x} = 7$
$x = 49$

$\sqrt{x} = ‐ 7$
Er is geen oplossing, want de wortel van een getal kan niet negatief zijn.

$\sqrt{x + 1} = 7$
$x + 1 = 49$
$x = 48$

$\frac{1}{x^{2}} = 7$
$x^{2} = \frac{1}{7}$
$x = \sqrt{\frac{1}{7}} = \frac{1}{7} \sqrt{7}$ of $x = ‐ \sqrt{\frac{1}{7}} = ‐ \frac{1}{7} \sqrt{7}$

Ontbinden

$x^{2} + 12 x + 36 = 16$
$x^{2} + 12 x + 20 = 0$

$x^{2} + 12 x + 20 = (x + 2) (x + 10)$

$x = ‐ 2$ of $x = ‐ 10$

$1 \cdot ‐ 24 = ‐ 24$	$‐ 1 \cdot 24 = ‐ 24$
$2 \cdot ‐ 12 = ‐ 24$	$‐ 2 \cdot 12 = ‐ 24$
$3 \cdot ‐ 8 = ‐ 24$	$‐ 3 \cdot 8 = ‐ 24$
$4 \cdot ‐ 6 = ‐ 24$	$‐ 4 \cdot 6 = ‐ 24$

$x^{2} + 5 x - 24 = (x + 8) (x - 3)$

$x^{2} + 5 x - 24 = 0$
$(x + 8) (x - 3) = 0$
$x = ‐ 8$ of $x = 3$

$(x + 4) (x - 1) = 0$ , dus $x = ‐ 4$ of $x = 1$

$(x + 6) (x - 4) = 0$ , dus $x = ‐ 6$ of $x = 4$

$(x + 6) (x + 4) = 0$ , dus $x = ‐ 6$ of $x = ‐ 4$

$x (x + 4) = 0$ , dus $x = 0$ of $x = ‐ 4$

$x^{2} + 2 x = 48$
$x^{2} + 2 x - 48 = 0$
$(x + 8) (x - 6) = 0$
$x = ‐ 8$ of $x = 6$

$x^{2} = 2 x$
$x^{2} - 2 x = 0$
$x (x - 2) = 0$
$x = 0$ of $x = 2$

$2 x^{2} + 4 x - 6 = 0$
$2 (x^{2} + 2 x - 3) = 0$
$2 (x + 3) (x - 1) = 0$
$x = ‐ 3$ of $x = 1$

$‐ x^{2} + 4 = ‐ 60$
$x^{2} = 64$
$x = 8$ of $x = ‐ 8$

$3 x^{2} = 15 x + 150$
$x^{2} = 5 x + 50$
$x^{2} - 5 x - 50 = 0$
$(x - 10) (x + 5) = 0$
$x = 10$ of $x = ‐ 5$

$(x - 1) (x + 3) = 117$
$x^{2} - x + 3 x - 3 = 117$
$x^{2} + 2 x - 120 = 0$
$(x - 10) (x + 12) = 0$
$x = 10$ of $x = ‐ 12$

$x^{3} + 2 x^{2} - 3 x = 0$
$x (x^{2} + 2 x - 3) = 0$
$x (x + 3) (x - 1) = 0$
$x = 0$ of $x = ‐ 3$ of $x = 1$

$x^{5} = 4 x^{4}$
$x^{5} - 4 x^{4} = 0$
$x^{4} (x - 4) = 0$
$x = 0$ of $x = 4$

${(x + 1)}^{2} = x + 3$
$x^{2} + 2 x + 1 = x + 3$
$x^{2} + x - 2 = 0$
$(x - 1) (x + 2) = 0$
$x = 1$ of $x = ‐ 2$

$x^{4} + 4 x^{3} + 4 x^{2} = 0$
$x^{2} (x^{2} + 4 x + 4) = 0$
$x^{2} {(x + 2)}^{2} = 0$
$x = 0$ of $x = ‐ 2$

...

$x + 4 \to x^{2} + 8 x + 16 \to x^{2} + 8 x + 15 \to (x + 3) (x + 5)$
$y + 10 \to y^{2} + 20 y + 100 \to y^{2} + 20 y + 99 \to (y + 9) (y + 11)$
$z + 11 \to z^{2} + 22 z + 121 \to z^{2} + 22 z + 120 \to (z + 10) (z + 12)$
$p + 1 \to p^{2} + 2 p + 1 \to p^{2} + 2 p \to p (p + 2)$

...

${(x + a)}^{2} = (x + a - 1) (x + a + 1)$

$x^{2} - 4 x - 21 = 0$
$(x + 3) (x - 7) = 0$
$x = ‐ 3$ of $x = 7$

$x^{2} - 4 x - 12 = 9$
$x^{2} - 4 x - 21 = 0$
Dus ook nu geldt $x = ‐ 3$ of $x = 7$

$x^{3} - 4 x^{2} - 21 = 0$
$x (x^{2} - 4 x - 21) = 0$
$x (x + 3) (x - 7) = 0$
$x = 0$ of $x = ‐ 3$ of $x = 7$