Solve n^2-26n

$$n ^ { 2 } - 26 n$$

Factor

$$n\left(n-26\right)$$

Solution Steps

Factor out n.

$$n\left(n-26\right)$$

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.

$$n^{2}-26n=0$$

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.

$$n=\frac{-\left(-26\right)±\sqrt{\left(-26\right)^{2}}}{2}$$

Take the square root of \left(-26\right)^{2}.

$$n=\frac{-\left(-26\right)±26}{2}$$

The opposite of -26 is 26.

$$n=\frac{26±26}{2}$$

Now solve the equation n=\frac{26±26}{2} when ± is plus. Add 26 to 26.

$$n=\frac{52}{2}$$

Divide 52 by 2.

$$n=26$$

Now solve the equation n=\frac{26±26}{2} when ± is minus. Subtract 26 from 26.

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

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 26 for x_{1} and 0 for x_{2}.

$$n^{2}-26n=\left(n-26\right)n$$

Evaluate

$$n\left(n-26\right)$$