(Isoleren)
\(-5 \sqrt{x} = -1\)

(Kwadrateren)
\((-5 \sqrt{x})^{2} = (-1)^{2}\)
\(25 x = 1\)
\(x = \frac{1}{25}\)

(Controleren)
\(x = \frac{1}{25}\) 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)
\(7 x - 9 = 2 \sqrt{x}\)

(Kwadrateren)
\((7 x - 9)^{2} = (2 \sqrt{x})^{2}\)
\(49 x^{2} - 126 x + 81 = 4 x\)

(Oplossen)
\(49 x^{2} + -130 x + 81 = 0\)
\(D = -130^{2} - 4 ⋅ 49 ⋅ 81 = 1024\)
\(x = {130 - \sqrt{1024} \over 2 ⋅ 49} ∨ x = {130 + \sqrt{1024} \over 2 ⋅ 49}\)
\(x = 1 ∨ x = {81 \over 49}\)

(Controleren)
\(x = 1\) voldoet niet, \(x = 1\frac{32}{49}\) voldoet.

(Isoleren)
\(x + 4 = \sqrt{6 x + 51}\)

(Kwadrateren)
\((x + 4)^{2} = (\sqrt{6 x + 51})^{2}\)
\(x^{2} + 8 x + 16 = 6 x + 51\)

(Oplossen)
\(1 x^{2} + 2 x + -35 = 0\)
\((x + 7) (x + -5) = 0\)
\(x = -7 ∨ x = 5\)

(Controleren)
\(x = -7\) voldoet niet, \(x = 5\) voldoet.

(Isoleren)
\(2 x - 6 = 4 \sqrt{3 x - 9}\)

(Kwadrateren)
\((2 x - 6)^{2} = (4 \sqrt{3 x - 9})^{2}\)
\(4 x^{2} - 24 x + 36 = 16 ⋅ (3 x - 9)\)
\(4 x^{2} - 24 x + 36 = 48 x - 144\)

(Oplossen)
\(4 x^{2} + -72 x + 180 = 0\)
\(1 x^{2} + -18 x + 45 = 0\)
\((x + -3) (x + -15) = 0\)
\(x = 3 ∨ x = 15\)

(Controleren)
Beide oplossingen voldoen.