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

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Answer 1 · 2017-03-05T03:52:57

#x=-1/2 or +5/2#

To solve this equation graphically first rewrite the equation as:

#4x^2-8x-5=0#

Consider the LHS to be#f(x)#

Now plot the graph of #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-# axis - as this is where #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:
#4x^2-8x-5=0 -> (2x+1)(2x-5)=0#

Thus: #x=-1/2 or +5/2#