# How do you solve the equation 4x^2-8x=5 by graphing?

##### 1 Answer
Mar 5, 2017

$x = - \frac{1}{2} \mathmr{and} + \frac{5}{2}$

#### Explanation:

To solve this equation graphically first rewrite the equation as:

$4 {x}^{2} - 8 x - 5 = 0$

Consider the LHS to be$f \left(x\right)$

Now plot the graph of $f \left(x\right)$ as below

graph{4x^2-8x-5 [-20.27, 20.28, -10.13, 10.14]}

The solutions for x can be seen as the intercepts of the graph with the $x -$ axis - as this is where $f \left(x\right) = 0$

By zooming in on the graph above, these can be sen to be:
-0.5 and +2.5

To check this result consider:
$4 {x}^{2} - 8 x - 5 = 0 \to \left(2 x + 1\right) \left(2 x - 5\right) = 0$

Thus: $x = - \frac{1}{2} \mathmr{and} + \frac{5}{2}$