Solve v^2-48v=

$$v ^ { 2 } - 48 v =$$

Factor

$$v\left(v-48\right)$$

Solution Steps

Factor out v.

$$v\left(v-48\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$v^{2}-48v=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$v=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}}}{2}$$

Take the square root of \left(-48\right)^{2}.

$$v=\frac{-\left(-48\right)±48}{2}$$

The opposite of -48 is 48.

$$v=\frac{48±48}{2}$$

Now solve the equation v=\frac{48±48}{2} when ± is plus. Add 48 to 48.

$$v=\frac{96}{2}$$

Divide 96 by 2.

$$v=48$$

Now solve the equation v=\frac{48±48}{2} when ± is minus. Subtract 48 from 48.

$$v=\frac{0}{2}$$

Divide 0 by 2.

$$v=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 48 for x_{1} and 0 for x_{2}.

$$v^{2}-48v=\left(v-48\right)v$$

Evaluate

$$v\left(v-48\right)$$