How do you solve $(x+6)(x-2)=9$ ?

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Answer 1 · 2016-03-14T17:34:44

The solutions are:
$x=3$
$x=-7$

$(x+6)(x−2)=9$

$(x) * (x) + x * (-2) +( 6) * (x) + 6 * (-2)=9$

$x^2 -2x + 6 x -12=9$

$x^2 +4x -12=9$

$x^2 +4x -12- 9= 0$

$x^2 +4x -21= 0$

The equation is of the form $color(blue)(ax^2+bx+c=0$ where:
$a=1, b=4, c= -21$

The Discriminant is given by:

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

$= (4)^2-(4*1 *-21)$

$= 16 + 84= 100$

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

$x =( -4 +-sqrt(100))/( 2* 1$

$x= ( -4 +10 )/ 2 = 6/2 = 3$

$x=( -4 -10 )/ 2 = -14/2 = -7$

How do you solve (x+6)(x-2)=9(x+6)(x-2)=9?