Solve for v v^2=u^2+2a(o-y)

$v^{2} = u^{2} + 2 a (o - y)$

Step 1

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

$v = \pm \sqrt{u^{2} + 2 a (o - y)}$

Step 2

Simplify $\pm \sqrt{u^{2} + 2 a (o - y)}$ .

Apply the distributive property.

$v = \pm \sqrt{u^{2} + 2 a o + 2 a (- y)}$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$v = \pm \sqrt{u^{2} + 2 a o + 2 \cdot - 1 a y}$

Multiply $2$ by $- 1$ .

$v = \pm \sqrt{u^{2} + 2 a o - 2 a y}$

Step 3

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.

$v = \sqrt{u^{2} + 2 a o - 2 a y}$

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

$v = - \sqrt{u^{2} + 2 a o - 2 a y}$

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

$v = \sqrt{u^{2} + 2 a o - 2 a y}$

$v = - \sqrt{u^{2} + 2 a o - 2 a y}$

$v = \sqrt{u^{2} + 2 a o - 2 a y}$

$v = - \sqrt{u^{2} + 2 a o - 2 a y}$