(Isoleren)
\(-6 \sqrt{x} = -1\)

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

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

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

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

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

(Isoleren)
\(-5 x - 4 = -9 \sqrt{x}\)

(Kwadrateren)
\((-5 x - 4)^{2} = (-9 \sqrt{x})^{2}\)
\(25 x^{2} + 40 x + 16 = 81 x\)

(Oplossen)
\(25 x^{2} + -41 x + 16 = 0\)
\(D = -41^{2} - 4 ⋅ 25 ⋅ 16 = 81\)
\(x = {41 - \sqrt{81} \over 2 ⋅ 25} ∨ x = {41 + \sqrt{81} \over 2 ⋅ 25}\)
\(x = {16 \over 25} ∨ x = 1\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x + 1 = \sqrt{3 x + 21}\)

(Kwadrateren)
\((x + 1)^{2} = (\sqrt{3 x + 21})^{2}\)
\(x^{2} + 2 x + 1 = 3 x + 21\)

(Oplossen)
\(1 x^{2} + -1 x + -20 = 0\)
\((x + 4) (x + -5) = 0\)
\(x = -4 ∨ x = 5\)

(Controleren)
\(x = 5\) voldoet, \(x = -4\) voldoet niet.

(Isoleren)
\(5 x - 7 = 9 \sqrt{2 x - 6}\)

(Kwadrateren)
\((5 x - 7)^{2} = (9 \sqrt{2 x - 6})^{2}\)
\(25 x^{2} - 70 x + 49 = 81 ⋅ (2 x - 6)\)
\(25 x^{2} - 70 x + 49 = 162 x - 486\)

(Oplossen)
\(25 x^{2} + -232 x + 535 = 0\)
\(D = -232^{2} - 4 ⋅ 25 ⋅ 535 = 324\)
\(x = {232 - \sqrt{324} \over 2 ⋅ 25} ∨ x = {232 + \sqrt{324} \over 2 ⋅ 25}\)
\(x = {107 \over 25} ∨ x = 5\)

(Controleren)
Beide oplossingen voldoen.