Solve for x v^2=v_0^2+2ax

$v^{2} = v_{0^{2}} + 2 a x$

Step 1

Rewrite the equation as $v_{0^{2}} + 2 a x = v^{2}$ .

$v_{0^{2}} + 2 a x = v^{2}$

Step 2

Subtract $v_{0^{2}}$ from both sides of the equation.

$2 a x = v^{2} - v_{0^{2}}$

Step 3

Divide each term in $2 a x = v^{2} - v_{0^{2}}$ by $2 a$ and simplify.

Divide each term in $2 a x = v^{2} - v_{0^{2}}$ by $2 a$ .

$\frac{2 a x}{2 a} = \frac{v^{2}}{2 a} + \frac{- v_{0^{2}}}{2 a}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a x}{2 a} = \frac{v^{2}}{2 a} + \frac{- v_{0^{2}}}{2 a}$

Rewrite the expression.

$\frac{a x}{a} = \frac{v^{2}}{2 a} + \frac{- v_{0^{2}}}{2 a}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a x}{a} = \frac{v^{2}}{2 a} + \frac{- v_{0^{2}}}{2 a}$

Divide $x$ by $1$ .

$x = \frac{v^{2}}{2 a} + \frac{- v_{0^{2}}}{2 a}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{v^{2}}{2 a} - \frac{v_{0^{2}}}{2 a}$