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

(Kwadrateren)
\((-6 \sqrt{x})^{2} = (-6)^{2}\)
\(36 x = 36\)
\(x = 1\)

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

(Kwadrateren)
\(x^{2} = 3 x + 54\)

(Oplossen)
\(1 x^{2} + -3 x + -54 = 0\)
\((x + 6) (x + -9) = 0\)
\(x = -6 ∨ x = 9\)

(Controleren)
\(x = -6\) voldoet niet, \(x = 9\) voldoet.

(Isoleren)
\(-7 x - 2 = -9 \sqrt{x}\)

(Kwadrateren)
\((-7 x - 2)^{2} = (-9 \sqrt{x})^{2}\)
\(49 x^{2} + 28 x + 4 = 81 x\)

(Oplossen)
\(49 x^{2} + -53 x + 4 = 0\)
\(D = -53^{2} - 4 ⋅ 49 ⋅ 4 = 2025\)
\(x = {53 - \sqrt{2025} \over 2 ⋅ 49} ∨ x = {53 + \sqrt{2025} \over 2 ⋅ 49}\)
\(x = {4 \over 49} ∨ x = 1\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x - 1 = \sqrt{4 x + 28}\)

(Kwadrateren)
\((x - 1)^{2} = (\sqrt{4 x + 28})^{2}\)
\(x^{2} - 2 x + 1 = 4 x + 28\)

(Oplossen)
\(1 x^{2} + -6 x + -27 = 0\)
\((x + 3) (x + -9) = 0\)
\(x = -3 ∨ x = 9\)

(Controleren)
\(x = -3\) voldoet niet, \(x = 9\) voldoet.

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

(Controleren)
Beide oplossingen voldoen.