Solve b-4k=left(2k-1right)^2

$$b-4k = { \left(2k-1 \right) }^{ 2 }$$

Solve for b

$$b=4k^{2}+1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2k-1\right)^{2}.

$$b-4k=4k^{2}-4k+1$$

Add 4k to both sides.

$$b=4k^{2}-4k+1+4k$$

Combine -4k and 4k to get 0.

$$b=4k^{2}+1$$

Solve for k

$$k=\frac{\sqrt{b-1}}{2}$$

$$k=-\frac{\sqrt{b-1}}{2}\text{, }b\geq 1$$