(Isoleren)
\(-9 \sqrt{x} = -4\)

(Kwadrateren)
\((-9 \sqrt{x})^{2} = (-4)^{2}\)
\(81 x = 16\)
\(x = \frac{16}{81}\)

(Controleren)
\(x = \frac{16}{81}\) voldoet.

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

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

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

(Isoleren)
\(-2 x + 5 = 3 \sqrt{x}\)

(Kwadrateren)
\((-2 x + 5)^{2} = (3 \sqrt{x})^{2}\)
\(4 x^{2} - 20 x + 25 = 9 x\)

(Oplossen)
\(4 x^{2} - 29 x + 25 = 0\)
\(D = (-29)^{2} - 4 ⋅ 4 ⋅ 25 = 441\)
\(x = {29 - \sqrt{441} \over 2 ⋅ 4} ∨ x = {29 + \sqrt{441} \over 2 ⋅ 4}\)
\(x = 1 ∨ x = 6\frac{1}{4}\)

(Controleren)
\(x = 1\) voldoet, \(x = 6\frac{1}{4}\) voldoet niet.

(Isoleren)
\(x + 1 = \sqrt{8 x - 7}\)

(Kwadrateren)
\((x + 1)^{2} = (\sqrt{8 x - 7})^{2}\)
\(x^{2} + 2 x + 1 = 8 x - 7\)

(Oplossen)
\(x^{2} - 6 x + 8 = 0\)
\((x - 2) (x - 4) = 0\)
\(x = 2 ∨ x = 4\)

(Controleren)
Beide oplossingen voldoen.

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

(Kwadrateren)
\((3 x - 2)^{2} = (2 \sqrt{3 x - 2})^{2}\)
\(9 x^{2} - 12 x + 4 = 4 ⋅ (3 x - 2)\)
\(9 x^{2} - 12 x + 4 = 12 x - 8\)

(Oplossen)
\(9 x^{2} - 24 x + 12 = 0\)
\(3 x^{2} - 8 x + 4 = 0\)
\(D = (-8)^{2} - 4 ⋅ 3 ⋅ 4 = 16\)
\(x = {8 - \sqrt{16} \over 2 ⋅ 3} ∨ x = {8 + \sqrt{16} \over 2 ⋅ 3}\)
\(x = \frac{2}{3} ∨ x = 2\)

(Controleren)
Beide oplossingen voldoen.