Solve n^2-7n

$$n ^ { 2 } - 7 n$$

Factor

$$n\left(n-7\right)$$

Solution Steps

Factor out n.

$$n\left(n-7\right)$$

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.

$$n^{2}-7n=0$$

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.

$$n=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2}$$

Take the square root of \left(-7\right)^{2}.

$$n=\frac{-\left(-7\right)±7}{2}$$

The opposite of -7 is 7.

$$n=\frac{7±7}{2}$$

Now solve the equation n=\frac{7±7}{2} when ± is plus. Add 7 to 7.

$$n=\frac{14}{2}$$

Divide 14 by 2.

$$n=7$$

Now solve the equation n=\frac{7±7}{2} when ± is minus. Subtract 7 from 7.

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

Divide 0 by 2.

$$n=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 7 for x_{1} and 0 for x_{2}.

$$n^{2}-7n=\left(n-7\right)n$$

Evaluate

$$n\left(n-7\right)$$