(Isoleren)
\(8 \sqrt{x} = 2\)

(Kwadrateren)
\((8 \sqrt{x})^{2} = 2^{2}\)
\(64 x = 4\)
\(x = \frac{1}{16}\)

(Controleren)
\(x = \frac{1}{16}\) voldoet.

(Kwadrateren)
\(x^{2} = 4 x + 32\)

(Oplossen)
\(1 x^{2} + -4 x + -32 = 0\)
\((x + 4) (x + -8) = 0\)
\(x = -4 ∨ x = 8\)

(Controleren)
\(x = -4\) voldoet niet, \(x = 8\) voldoet.

(Isoleren)
\(-6 x + 4 = 2 \sqrt{x}\)

(Kwadrateren)
\((-6 x + 4)^{2} = (2 \sqrt{x})^{2}\)
\(36 x^{2} - 48 x + 16 = 4 x\)

(Oplossen)
\(36 x^{2} + -52 x + 16 = 0\)
\(9 x^{2} + -13 x + 4 = 0\)
\(D = -13^{2} - 4 ⋅ 9 ⋅ 4 = 25\)
\(x = {13 - \sqrt{25} \over 2 ⋅ 9} ∨ x = {13 + \sqrt{25} \over 2 ⋅ 9}\)
\(x = {4 \over 9} ∨ x = 1\)

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

(Isoleren)
\(x + 1 = \sqrt{4 x + 49}\)

(Kwadrateren)
\((x + 1)^{2} = (\sqrt{4 x + 49})^{2}\)
\(x^{2} + 2 x + 1 = 4 x + 49\)

(Oplossen)
\(1 x^{2} + -2 x + -48 = 0\)
\((x + 6) (x + -8) = 0\)
\(x = -6 ∨ x = 8\)

(Controleren)
\(x = 8\) voldoet, \(x = -6\) voldoet niet.

(Isoleren)
\(8 x - 8 = 2 \sqrt{7 x - 7}\)

(Kwadrateren)
\((8 x - 8)^{2} = (2 \sqrt{7 x - 7})^{2}\)
\(64 x^{2} - 128 x + 64 = 4 ⋅ (7 x - 7)\)
\(64 x^{2} - 128 x + 64 = 28 x - 28\)

(Oplossen)
\(64 x^{2} + -156 x + 92 = 0\)
\(16 x^{2} + -39 x + 23 = 0\)
\(D = -39^{2} - 4 ⋅ 16 ⋅ 23 = 49\)
\(x = {39 - \sqrt{49} \over 2 ⋅ 16} ∨ x = {39 + \sqrt{49} \over 2 ⋅ 16}\)
\(x = 1 ∨ x = {23 \over 16}\)

(Controleren)
Beide oplossingen voldoen.