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

(Kwadrateren)
\((8 \sqrt{x})^{2} = 3^{2}\)
\(64 x = 9\)
\(x = \frac{9}{64}\)

(Controleren)
\(x = \frac{9}{64}\) voldoet.

(Kwadrateren)
\(x^{2} = -6 x + 16\)

(Oplossen)
\(1 x^{2} + 6 x + -16 = 0\)
\((x + 8) (x + -2) = 0\)
\(x = -8 ∨ x = 2\)

(Controleren)
\(x = -8\) voldoet niet, \(x = 2\) voldoet.

(Isoleren)
\(-3 x + 4 = 4 \sqrt{x}\)

(Kwadrateren)
\((-3 x + 4)^{2} = (4 \sqrt{x})^{2}\)
\(9 x^{2} - 24 x + 16 = 16 x\)

(Oplossen)
\(9 x^{2} + -40 x + 16 = 0\)
\(D = -40^{2} - 4 ⋅ 9 ⋅ 16 = 1024\)
\(x = {40 - \sqrt{1024} \over 2 ⋅ 9} ∨ x = {40 + \sqrt{1024} \over 2 ⋅ 9}\)
\(x = {4 \over 9} ∨ x = 4\)

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

(Isoleren)
\(x - 5 = \sqrt{5 x - 29}\)

(Kwadrateren)
\((x - 5)^{2} = (\sqrt{5 x - 29})^{2}\)
\(x^{2} - 10 x + 25 = 5 x - 29\)

(Oplossen)
\(1 x^{2} + -15 x + 54 = 0\)
\((x + -6) (x + -9) = 0\)
\(x = 6 ∨ x = 9\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(9 x - 7 = 3 \sqrt{9 x - 9}\)

(Kwadrateren)
\((9 x - 7)^{2} = (3 \sqrt{9 x - 9})^{2}\)
\(81 x^{2} - 126 x + 49 = 9 ⋅ (9 x - 9)\)
\(81 x^{2} - 126 x + 49 = 81 x - 81\)

(Oplossen)
\(81 x^{2} + -207 x + 130 = 0\)
\(D = -207^{2} - 4 ⋅ 81 ⋅ 130 = 729\)
\(x = {207 - \sqrt{729} \over 2 ⋅ 81} ∨ x = {207 + \sqrt{729} \over 2 ⋅ 81}\)
\(x = {10 \over 9} ∨ x = {13 \over 9}\)

(Controleren)
Beide oplossingen voldoen.