(Isoleren)
\(6 \sqrt{x} = 7\)

(Kwadrateren)
\((6 \sqrt{x})^{2} = 7^{2}\)
\(36 x = 49\)
\(x = 1\frac{13}{36}\)

(Controleren)
\(x = 1\frac{13}{36}\) voldoet.

(Kwadrateren)
\(x^{2} = -5 x + 36\)

(Oplossen)
\(1 x^{2} + 5 x + -36 = 0\)
\((x + 9) (x + -4) = 0\)
\(x = -9 ∨ x = 4\)

(Controleren)
\(x = -9\) voldoet niet, \(x = 4\) 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)
\(x + 3 = \sqrt{8 x + 33}\)

(Kwadrateren)
\((x + 3)^{2} = (\sqrt{8 x + 33})^{2}\)
\(x^{2} + 6 x + 9 = 8 x + 33\)

(Oplossen)
\(1 x^{2} + -2 x + -24 = 0\)
\((x + 4) (x + -6) = 0\)
\(x = -4 ∨ x = 6\)

(Controleren)
\(x = 6\) voldoet, \(x = -4\) voldoet niet.

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

(Kwadrateren)
\((2 x - 2)^{2} = (3 \sqrt{3 x - 5})^{2}\)
\(4 x^{2} - 8 x + 4 = 9 ⋅ (3 x - 5)\)
\(4 x^{2} - 8 x + 4 = 27 x - 45\)

(Oplossen)
\(4 x^{2} + -35 x + 49 = 0\)
\(D = -35^{2} - 4 ⋅ 4 ⋅ 49 = 441\)
\(x = {35 - \sqrt{441} \over 2 ⋅ 4} ∨ x = {35 + \sqrt{441} \over 2 ⋅ 4}\)
\(x = {7 \over 4} ∨ x = 7\)

(Controleren)
Beide oplossingen voldoen.