Evaluate v^2=v_0^2+2ax

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

Take the square root of both sides of the equation to eliminate the exponent on the left side.

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

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

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

Next, use the negative value of the $\pm$ to find the second solution.

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

The complete solution is the result of both the positive and negative portions of the solution.

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

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

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

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