(Isoleren)
\(-5 \sqrt{x} = -5\)

(Kwadrateren)
\((-5 \sqrt{x})^{2} = (-5)^{2}\)
\(25 x = 25\)
\(x = 1\)

(Controleren)
\(x = 1\) voldoet.

(Kwadrateren)
\(x^{2} = 4 x + 32\)

(Oplossen)
\(x^{2} - 4 x - 32 = 0\)
\((x + 4) (x - 8) = 0\)
\(x = -4 ∨ x = 8\)

(Controleren)
\(x = -4\) voldoet niet, \(x = 8\) voldoet.

(Isoleren)
\(4 x - 8 = -4 \sqrt{x}\)

(Kwadrateren)
\((4 x - 8)^{2} = (-4 \sqrt{x})^{2}\)
\(16 x^{2} - 64 x + 64 = 16 x\)

(Oplossen)
\(16 x^{2} - 80 x + 64 = 0\)
\(x^{2} - 5 x + 4 = 0\)
\((x - 1) (x - 4) = 0\)
\(x = 1 ∨ x = 4\)

(Controleren)
\(x = 1\) voldoet, \(x = 4\) voldoet niet.

(Isoleren)
\(x + 1 = \sqrt{9 x - 11}\)

(Kwadrateren)
\((x + 1)^{2} = (\sqrt{9 x - 11})^{2}\)
\(x^{2} + 2 x + 1 = 9 x - 11\)

(Oplossen)
\(x^{2} - 7 x + 12 = 0\)
\((x - 3) (x - 4) = 0\)
\(x = 3 ∨ x = 4\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(8 x - 9 = 2 \sqrt{8 x - 9}\)

(Kwadrateren)
\((8 x - 9)^{2} = (2 \sqrt{8 x - 9})^{2}\)
\(64 x^{2} - 144 x + 81 = 4 ⋅ (8 x - 9)\)
\(64 x^{2} - 144 x + 81 = 32 x - 36\)

(Oplossen)
\(64 x^{2} - 176 x + 117 = 0\)
\(D = (-176)^{2} - 4 ⋅ 64 ⋅ 117 = 1\,024\)
\(x = {176 - \sqrt{1\,024} \over 2 ⋅ 64} ∨ x = {176 + \sqrt{1\,024} \over 2 ⋅ 64}\)
\(x = 1\frac{1}{8} ∨ x = 1\frac{5}{8}\)

(Controleren)
Beide oplossingen voldoen.