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

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Answer 1 · 2017-03-05T03:52:57

$x = - \frac{1}{2} or + \frac{5}{2}$ $x=-1/2 or +5/2$

To solve this equation graphically first rewrite the equation as:

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

Consider the LHS to be $f (x)$ $f(x)$

Now plot the graph of $f (x)$ $f(x)$ 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 $x -$ $x-$ axis - as this is where $f (x) = 0$ $f(x)=0$

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

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

Thus: $x = - \frac{1}{2} or + \frac{5}{2}$ $x=-1/2 or +5/2$

How do you solve the equation 4x^2-8x=54x2−8x=54x^2-8x=5 by graphing?