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

(Kwadrateren)
\((7 \sqrt{x})^{2} = 2^{2}\)
\(49 x = 4\)
\(x = \frac{4}{49}\)

(Controleren)
\(x = \frac{4}{49}\) voldoet.

(Kwadrateren)
\(x^{2} = 3 x + 18\)

(Oplossen)
\(1 x^{2} + -3 x + -18 = 0\)
\((x + 3) (x + -6) = 0\)
\(x = -3 ∨ x = 6\)

(Controleren)
\(x = -3\) voldoet niet, \(x = 6\) voldoet.

(Isoleren)
\(-8 x + 3 = 2 \sqrt{x}\)

(Kwadrateren)
\((-8 x + 3)^{2} = (2 \sqrt{x})^{2}\)
\(64 x^{2} - 48 x + 9 = 4 x\)

(Oplossen)
\(64 x^{2} + -52 x + 9 = 0\)
\(D = -52^{2} - 4 ⋅ 64 ⋅ 9 = 400\)
\(x = {52 - \sqrt{400} \over 2 ⋅ 64} ∨ x = {52 + \sqrt{400} \over 2 ⋅ 64}\)
\(x = {1 \over 4} ∨ x = {9 \over 16}\)

(Controleren)
\(x = \frac{1}{4}\) voldoet, \(x = \frac{9}{16}\) voldoet niet.

(Isoleren)
\(x + 8 = \sqrt{8 x + 52}\)

(Kwadrateren)
\((x + 8)^{2} = (\sqrt{8 x + 52})^{2}\)
\(x^{2} + 16 x + 64 = 8 x + 52\)

(Oplossen)
\(1 x^{2} + 8 x + 12 = 0\)
\((x + 6) (x + 2) = 0\)
\(x = -6 ∨ x = -2\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(7 x - 5 = 8 \sqrt{3 x - 5}\)

(Kwadrateren)
\((7 x - 5)^{2} = (8 \sqrt{3 x - 5})^{2}\)
\(49 x^{2} - 70 x + 25 = 64 ⋅ (3 x - 5)\)
\(49 x^{2} - 70 x + 25 = 192 x - 320\)

(Oplossen)
\(49 x^{2} + -262 x + 345 = 0\)
\(D = -262^{2} - 4 ⋅ 49 ⋅ 345 = 1024\)
\(x = {262 - \sqrt{1024} \over 2 ⋅ 49} ∨ x = {262 + \sqrt{1024} \over 2 ⋅ 49}\)
\(x = {115 \over 49} ∨ x = 3\)

(Controleren)
Beide oplossingen voldoen.