How do you solve $x^2 – 3x – 23 = 5$ ?

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Answer 1 · 2016-03-29T17:02:23

The solutions are:
$x= color(blue)(7$

$x = color(blue)(-4$

$x^2 - 3x - 23 = 5$

$x^2 - 3x - 23 - 5 = 0$

$x^2 - 3x - 28 = 0$

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=1, b=-3, c=-28$

The Discriminant is given by:

$Delta=b^2-4*a*c$

$= (-3)^2-(4*1* ( -28))$

$= 9 + 112= 121$

The solutions are found using the formula
$x=(-b+-sqrtDelta)/(2*a)$

$x = (-(-3)+-sqrt(121))/(2*1) = (3+- 11)/2$

$x = (3+ 11)/2 = 14/2 = color(blue)(7$

$x = (3-11)/2 = -8/2 = color(blue)(-4$

How do you solve x^2 – 3x – 23 = 5x^2 – 3x – 23 = 5?