(Isoleren)
\(-8\sqrt{t}=-1\)

(Kwadrateren)
\((-8\sqrt{t})^2=(-1)^2\)
\(64t=1\)
\(t=\frac{1}{64}\)

(Controleren)
\(t=\frac{1}{64}\) voldoet.

(Kwadrateren)
\(x^2=2x+8\)

(Oplossen)
\(x^2-2x-8=0\)
\((x+2)(x-4)=0\)
\(x=-2∨x=4\)

(Controleren)
\(x=-2\) voldoet niet, \(x=4\) voldoet.

(Isoleren)
\(6x-8=-2\sqrt{x}\)

(Kwadrateren)
\((6x-8)^2=(-2\sqrt{x})^2\)
\(36x^2-96x+64=4x\)

(Oplossen)
\(36x^2-100x+64=0\)
\(9x^2-25x+16=0\)
\(D=(-25)^2-4⋅9⋅16=49\)
\(x={25-\sqrt{49} \over 2⋅9}∨x={25+\sqrt{49} \over 2⋅9}\)
\(x=1∨x=1\frac{7}{9}\)

(Controleren)
\(x=1\) voldoet, \(x=1\frac{7}{9}\) voldoet niet.

(Isoleren)
\(t-4=\sqrt{3t-12}\)

(Kwadrateren)
\((t-4)^2=(\sqrt{3t-12})^2\)
\(t^2-8t+16=3t-12\)

(Oplossen)
\(t^2-11t+28=0\)
\((t-4)(t-7)=0\)
\(t=4∨t=7\)

(Controleren)
Beide oplossingen voldoen.

(Isoleren)
\(8t-8=3\sqrt{5t-5}\)

(Kwadrateren)
\((8t-8)^2=(3\sqrt{5t-5})^2\)
\(64t^2-128t+64=9⋅(5t-5)\)
\(64t^2-128t+64=45t-45\)

(Oplossen)
\(64t^2-173t+109=0\)
\(D=(-173)^2-4⋅64⋅109=2\,025\)
\(t={173-\sqrt{2\,025} \over 2⋅64}∨t={173+\sqrt{2\,025} \over 2⋅64}\)
\(t=1∨t=1\frac{45}{64}\)

(Controleren)
Beide oplossingen voldoen.