How do you solve #x^2+8x-5=0# graphically?

1 Answer
Jun 28, 2017

Plot points and identify where the parabola hits the #x# axis

#x=-8.5826# and #x=0.5826#

Explanation:

First, plotting some points, gives

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These points reveal the general shape of the graph.

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Sketching reveals that the solution is around #x~~-8.5# and #x~~0.5#. However, the exact zero still isn't known because of inaccuracies in sketching.

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Finding the exact roots, or zeroes of this equation requires and algebraic solution. Using the quadratic equation gives

#x=(-8+-sqrt((8)^2-4(1)(-5)))/(2(1))#

#x=(-8+-sqrt(84))/2#

#x=(-8+-2sqrt(21))/2#

#x=-8/2+-2sqrt(21)/2#

#x=--4+-sqrt(21)#

#x=-8.5826# and #x=0.5826#