# How do you solve x^2 - 21x - 72 = 0?

Mar 22, 2016

this quadratic equation can be factored as $\left(x - 24\right) \left(x + 3\right) = 0$

now that we have a product of two factors equal to zero, that means that at least one of the factors MUST be equal to zero.
so

we have $x - 24 = 0 \mathmr{and} x + 3 = 0$
this means that we have now reduced this to a matter of solving 2 linear equations.
and $x = 24 \mathmr{and} x = - 3$ are two different solutions for x

Mar 22, 2016

-3 and 24

#### Explanation:

$y = {x}^{2} - 21 x - 72 = 0$
Use the new Transforming Method (Google, Yahoo Search).
The 2 real roots have opposite signs because ac < 0.
Compose factor pairs of (-72) --> (-2, 36)(-3, 24). This last sum is
(24 - 3) = 21 = -b. Then, the 2 real roots are: -3 and 24.

NOTE
There is no need to factor by grouping and solving the 2 binomials.