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How do you solve $x^2 - 2x - 18 = 0$ using the quadratic formula?

1 Answer

Aug 6, 2015

$x= 1+sqrt(19)$ or $x=1-sqrt(19)$
(see below for solution using the quadratic formula)

Explanation:

The quadratic formula says that for any quadratic in the form:
$color(white)("XXXX")$ $ax^2+bx+c=0$
the roots (solution) can be determined by:
$color(white)("XXXX")$ $x= (-b+-sqrt(b^2-4ac))/(2a)$

For the given equation $x^2-2x-18=0$
$a=1$ $color(white)("XXXX")$ $b=-2$ $color(white)("XXXX")$ $c=-18$

So the solutions are
$color(white)("XXXX")$ $x=(2+-sqrt((-2)^2-4(1)(-18)))/(2(1))$

$color(white)("XXXX")$ $color(white)("XXXX")$ $= (2+-sqrt(4+72))/2$

$color(white)("XXXX")$ $color(white)("XXXX")$ $=(2+-sqrt(76))/2$

$color(white)("XXXX")$ $color(white)("XXXX")$ $=(2+-2sqrt(19))/2$

$color(white)("XXXX")$ $color(white)("XXXX")$ $= 1+-sqrt(19)$

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