$\"\"$

The equation is $\"\"$ .

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

Graph the related function $\"\"$ .

$\"graph$

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, $\"\"$ .Since $\"\"$ is positive and $\"\"$ is negative, so m and p are both negative.You need to find two negative factors with a sum of $\"\"$ and a product of $\"\"$ .

Make a list of the factors of 12 and look for the of factors with the sum of $\"\"$ .

$\"\"$

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

The equation, $\"\"$ has no solution.