Solve y^2=u^2+2as

$$y ^ { 2 } = u ^ { 2 } + 2 a s$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{u^{2}-y^{2}}{2s}\text{, }&s\neq 0\\a\in \mathrm{R}\text{, }&s=0\text{ and }|y|=|u|\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$u^{2}+2as=y^{2}$$

Subtract u^{2} from both sides.

$$2as=y^{2}-u^{2}$$

The equation is in standard form.

$$2sa=y^{2}-u^{2}$$

Divide both sides by 2s.

$$\frac{2sa}{2s}=\frac{\left(y-u\right)\left(y+u\right)}{2s}$$

Dividing by 2s undoes the multiplication by 2s.

$$a=\frac{\left(y-u\right)\left(y+u\right)}{2s}$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{u^{2}-y^{2}}{2a}\text{, }&a\neq 0\\s\in \mathrm{R}\text{, }&a=0\text{ and }|y|=|u|\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$u^{2}+2as=y^{2}$$

Subtract u^{2} from both sides.

$$2as=y^{2}-u^{2}$$

Divide both sides by 2a.

$$\frac{2as}{2a}=\frac{\left(y-u\right)\left(y+u\right)}{2a}$$

Dividing by 2a undoes the multiplication by 2a.

$$s=\frac{\left(y-u\right)\left(y+u\right)}{2a}$$