# How do you solve the equation by graphing x^2 - 5x - 24 = 0?

Nov 23, 2017

$x = - 3$
$x = 8$

#### Explanation:

The quadratic can be solved by graphing. The solutions are where the graph crosses the x-axis.

graph{x^2-5x-24 [-16.02, 16.01, -8.02, 8]}

As you can see from the graph, it crosses the x axis at $\left(- 3 , 0\right)$ and at $\left(8 , 0\right)$

The answers are $x = - 3$ and $x = 8$

This can also be solved by factorising the polynomial.

${x}^{2} - 5 x - 24 = 0$

The factors are 8 and 3 because they multiply to make 24 and subtract to make 8.

$\left(x + 3\right) \left(x - 8\right) = 0$

This means that the graph crosses the x-axis at $- 3$ and at $8$.