Pre-Algebra Examples

$Q = v B^{2} + t B$

Step 1

Rewrite the equation as $v B^{2} + t B = Q$ .

$v B^{2} + t B = Q$

Step 2

Subtract $Q$ from both sides of the equation.

$v B^{2} + t B - Q = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = v$ , $b = t$ , and $c = - Q$ into the quadratic formula and solve for $B$ .

$\frac{- t \pm \sqrt{t^{2} - 4 \cdot (v \cdot (- Q))}}{2 v}$

Step 5

Multiply $- 1$ by $- 4$ .

$B = \frac{- t \pm \sqrt{t^{2} + 4 v Q}}{2 v}$

Step 6

The final answer is the combination of both solutions.

$B = - \frac{t - \sqrt{t^{2} + 4 v Q}}{2 v}$

$B = - \frac{t + \sqrt{t^{2} + 4 v Q}}{2 v}$