How do you solve $x^{2} + 8 x - 5 = 0$ $x^2+8x-5=0$ graphically?

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How do you solve $x^{2} + 8 x - 5 = 0$ $x^2+8x-5=0$ graphically?

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Answer 1 · 2017-06-28T04:27:21

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

$x = - 8.5826$ $x=-8.5826$ and $x = 0.5826$ $x=0.5826$

Explanation:

First, plotting some points, gives

![Desmos.com](useruploads.socratic.org)

These points reveal the general shape of the graph.

![Desmos.com](useruploads.socratic.org)

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

![Desmos.com](useruploads.socratic.org)

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

$x = \frac{- 8 \pm \sqrt{{(8)}^{2} - 4 (1) (- 5)}}{2 (1)}$ $x=(-8+-sqrt((8)^2-4(1)(-5)))/(2(1))$

$x = \frac{- 8 \pm \sqrt{84}}{2}$ $x=(-8+-sqrt(84))/2$

$x = \frac{- 8 \pm 2 \sqrt{21}}{2}$ $x=(-8+-2sqrt(21))/2$

$x = - \frac{8}{2} \pm 2 \frac{\sqrt{21}}{2}$ $x=-8/2+-2sqrt(21)/2$

$x = - - 4 \pm \sqrt{21}$ $x=--4+-sqrt(21)$

$x = - 8.5826$ $x=-8.5826$ and $x = 0.5826$ $x=0.5826$

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How do you solve $x^{2} + 8 x - 5 = 0$ $x^2+8x-5=0$ graphically?

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