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

(Kwadrateren)
\((2\sqrt{x})^2=5^2\)
\(4x=25\)
\(x=6\frac{1}{4}\)

(Controleren)
\(x=6\frac{1}{4}\) voldoet.

(Kwadrateren)
\(x^2=-x+56\)

(Oplossen)
\(x^2+x-56=0\)
\((x+8)(x-7)=0\)
\(x=-8∨x=7\)

(Controleren)
\(x=-8\) voldoet niet, \(x=7\) voldoet.

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

(Kwadrateren)
\((-6x-2)^2=(-7\sqrt{x})^2\)
\(36x^2+24x+4=49x\)

(Oplossen)
\(36x^2-25x+4=0\)
\(D=(-25)^2-4⋅36⋅4=49\)
\(x={25-\sqrt{49} \over 2⋅36}∨x={25+\sqrt{49} \over 2⋅36}\)
\(x=\frac{1}{4}∨x=\frac{4}{9}\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(x+8=\sqrt{2x+16}\)

(Kwadrateren)
\((x+8)^2=(\sqrt{2x+16})^2\)
\(x^2+16x+64=2x+16\)

(Oplossen)
\(x^2+14x+48=0\)
\((x+8)(x+6)=0\)
\(x=-8∨x=-6\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(5x-4=8\sqrt{2x-4}\)

(Kwadrateren)
\((5x-4)^2=(8\sqrt{2x-4})^2\)
\(25x^2-40x+16=64⋅(2x-4)\)
\(25x^2-40x+16=128x-256\)

(Oplossen)
\(25x^2-168x+272=0\)
\(D=(-168)^2-4⋅25⋅272=1\,024\)
\(x={168-\sqrt{1\,024} \over 2⋅25}∨x={168+\sqrt{1\,024} \over 2⋅25}\)
\(x=2\frac{18}{25}∨x=4\)

(Controleren)
Beide oplossingen voldoen.