## Algebra## Polynomial Equations |

## Can all quadratic equations be solved by factoring? |

Don’t be fooled: Not all quadratic equations can be solved by factoring. For example, *x*^{2} - 3*x* = 3 is not solvable with this method. One way to solve quadratic equations is by completing the square; still another method is to graph the solution (a quadratic graph forms a parabola—a U-shaped line seen on the graph). But one of the most well-known ways is by using the quadratic formula (see below).

For example, if we want to find the roots of the polynomial *x*^{2} + 2*x* - 7, we can replace the “corresponding” numbers from the initial equation into the quadratic equation; thus, *a* = 1, *b* = 2, and *c* = -7. Substituting these numbers into the quadratic formula, we solve for:

That equals