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

(Kwadrateren)
\((7 \sqrt{x})^{2} = 5^{2}\)
\(49 x = 25\)
\(x = \frac{25}{49}\)

(Controleren)
\(x = \frac{25}{49}\) voldoet.

(Kwadrateren)
\(x^{2} = -2 x + 35\)

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

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

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

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x + 7 = \sqrt{8 x + 41}\)

(Kwadrateren)
\((x + 7)^{2} = (\sqrt{8 x + 41})^{2}\)
\(x^{2} + 14 x + 49 = 8 x + 41\)

(Oplossen)
\(1 x^{2} + 6 x + 8 = 0\)
\((x + 4) (x + 2) = 0\)
\(x = -4 ∨ x = -2\)

(Controleren)
Beide oplossingen voldoen.

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

(Kwadrateren)
\((4 x - 4)^{2} = (2 \sqrt{3 x - 3})^{2}\)
\(16 x^{2} - 32 x + 16 = 4 ⋅ (3 x - 3)\)
\(16 x^{2} - 32 x + 16 = 12 x - 12\)

(Oplossen)
\(16 x^{2} + -44 x + 28 = 0\)
\(4 x^{2} + -11 x + 7 = 0\)
\(D = -11^{2} - 4 ⋅ 4 ⋅ 7 = 9\)
\(x = {11 - \sqrt{9} \over 2 ⋅ 4} ∨ x = {11 + \sqrt{9} \over 2 ⋅ 4}\)
\(x = 1 ∨ x = {7 \over 4}\)

(Controleren)
Beide oplossingen voldoen.