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

(Kwadrateren)
\((5 \sqrt{x})^{2} = 3^{2}\)
\(25 x = 9\)
\(x = \frac{9}{25}\)

(Controleren)
\(x = \frac{9}{25}\) voldoet.

(Kwadrateren)
\(x^{2} = -7 x + 18\)

(Oplossen)
\(1 x^{2} + 7 x + -18 = 0\)
\((x + 9) (x + -2) = 0\)
\(x = -9 ∨ x = 2\)

(Controleren)
\(x = -9\) voldoet niet, \(x = 2\) voldoet.

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

(Kwadrateren)
\((-2 x - 5)^{2} = (-7 \sqrt{x})^{2}\)
\(4 x^{2} + 20 x + 25 = 49 x\)

(Oplossen)
\(4 x^{2} + -29 x + 25 = 0\)
\(D = -29^{2} - 4 ⋅ 4 ⋅ 25 = 441\)
\(x = {29 - \sqrt{441} \over 2 ⋅ 4} ∨ x = {29 + \sqrt{441} \over 2 ⋅ 4}\)
\(x = 1 ∨ x = {25 \over 4}\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x - 4 = \sqrt{6 x - 29}\)

(Kwadrateren)
\((x - 4)^{2} = (\sqrt{6 x - 29})^{2}\)
\(x^{2} - 8 x + 16 = 6 x - 29\)

(Oplossen)
\(1 x^{2} + -14 x + 45 = 0\)
\((x + -5) (x + -9) = 0\)
\(x = 5 ∨ x = 9\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(4 x - 9 = 5 \sqrt{3 x - 9}\)

(Kwadrateren)
\((4 x - 9)^{2} = (5 \sqrt{3 x - 9})^{2}\)
\(16 x^{2} - 72 x + 81 = 25 ⋅ (3 x - 9)\)
\(16 x^{2} - 72 x + 81 = 75 x - 225\)

(Oplossen)
\(16 x^{2} + -147 x + 306 = 0\)
\(D = -147^{2} - 4 ⋅ 16 ⋅ 306 = 2025\)
\(x = {147 - \sqrt{2025} \over 2 ⋅ 16} ∨ x = {147 + \sqrt{2025} \over 2 ⋅ 16}\)
\(x = {51 \over 16} ∨ x = 6\)

(Controleren)
Beide oplossingen voldoen.