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

(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)
\(3 x + 5 = 8 \sqrt{x}\)

(Kwadrateren)
\((3 x + 5)^{2} = (8 \sqrt{x})^{2}\)
\(9 x^{2} + 30 x + 25 = 64 x\)

(Oplossen)
\(9 x^{2} + -34 x + 25 = 0\)
\(D = -34^{2} - 4 ⋅ 9 ⋅ 25 = 256\)
\(x = {34 - \sqrt{256} \over 2 ⋅ 9} ∨ x = {34 + \sqrt{256} \over 2 ⋅ 9}\)
\(x = 1 ∨ x = {25 \over 9}\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x + 4 = \sqrt{5 x + 34}\)

(Kwadrateren)
\((x + 4)^{2} = (\sqrt{5 x + 34})^{2}\)
\(x^{2} + 8 x + 16 = 5 x + 34\)

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

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

(Isoleren)
\(7 x - 2 = 5 \sqrt{3 x - 2}\)

(Kwadrateren)
\((7 x - 2)^{2} = (5 \sqrt{3 x - 2})^{2}\)
\(49 x^{2} - 28 x + 4 = 25 ⋅ (3 x - 2)\)
\(49 x^{2} - 28 x + 4 = 75 x - 50\)

(Oplossen)
\(49 x^{2} + -103 x + 54 = 0\)
\(D = -103^{2} - 4 ⋅ 49 ⋅ 54 = 25\)
\(x = {103 - \sqrt{25} \over 2 ⋅ 49} ∨ x = {103 + \sqrt{25} \over 2 ⋅ 49}\)
\(x = 1 ∨ x = {54 \over 49}\)

(Controleren)
Beide oplossingen voldoen.