(Isoleren)
\(-3 \sqrt{x} = -2\)

(Kwadrateren)
\((-3 \sqrt{x})^{2} = (-2)^{2}\)
\(9 x = 4\)
\(x = \frac{4}{9}\)

(Controleren)
\(x = \frac{4}{9}\) voldoet.

(Kwadrateren)
\(x^{2} = x + 30\)

(Oplossen)
\(x^{2} - x - 30 = 0\)
\((x + 5) (x - 6) = 0\)
\(x = -5 ∨ x = 6\)

(Controleren)
\(x = -5\) voldoet niet, \(x = 6\) voldoet.

(Isoleren)
\(-6 x - 2 = -8 \sqrt{x}\)

(Kwadrateren)
\((-6 x - 2)^{2} = (-8 \sqrt{x})^{2}\)
\(36 x^{2} + 24 x + 4 = 64 x\)

(Oplossen)
\(36 x^{2} - 40 x + 4 = 0\)
\(9 x^{2} - 10 x + 1 = 0\)
\(D = (-10)^{2} - 4 ⋅ 9 ⋅ 1 = 64\)
\(x = {10 - \sqrt{64} \over 2 ⋅ 9} ∨ x = {10 + \sqrt{64} \over 2 ⋅ 9}\)
\(x = \frac{1}{9} ∨ x = 1\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x - 1 = \sqrt{5 x - 11}\)

(Kwadrateren)
\((x - 1)^{2} = (\sqrt{5 x - 11})^{2}\)
\(x^{2} - 2 x + 1 = 5 x - 11\)

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

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(6 x - 6 = 3 \sqrt{6 x - 8}\)

(Kwadrateren)
\((6 x - 6)^{2} = (3 \sqrt{6 x - 8})^{2}\)
\(36 x^{2} - 72 x + 36 = 9 ⋅ (6 x - 8)\)
\(36 x^{2} - 72 x + 36 = 54 x - 72\)

(Oplossen)
\(36 x^{2} - 126 x + 108 = 0\)
\(2 x^{2} - 7 x + 6 = 0\)
\(D = (-7)^{2} - 4 ⋅ 2 ⋅ 6 = 1\)
\(x = {7 - \sqrt{1} \over 2 ⋅ 2} ∨ x = {7 + \sqrt{1} \over 2 ⋅ 2}\)
\(x = 1\frac{1}{2} ∨ x = 2\)

(Controleren)
Beide oplossingen voldoen.