The standard form of quadratic equation in x - variables is , where .

The equation is .

Subtract 13 from each side.

.

Graph the related function .

Observe the graph, the graph does not intersect the x - axis. So the equation has no real number solutions. The solution set is .

To check the solution by factoring method as follows:

The polynomial is .

The general quadratic expression form is .

In the above trinomial, . You need to find two numbers with a sum of 8 and a product of  . Make a list of the factors of 26 and look for the of factors with the sum of 8.

There is no factors with a sum of 8. So, the quadratic expression cannot be factored using integers. Therefore, is prime.

The equation, has no solution.