can anybody please solve 3x^2-6x-9=0 using the quadratic formula!?

the quadric equation: x = [-b ± √(b² - 4ac)]/2a
3x² - 6x - 9 = 0
x = (6 ± √(36 + 4(3)(9))) / 6
x = (6 ± 12) / 6
x = 3, -1

Answer: 3, -1

a) Solve by factorising x2 - 6x + 8 = 0 Break up the 8 into its factors, and then identify two which add to give -6 and multiply to give 8. You should get -2 and -4. Therefore, (x-2)(x-4) = 0 --- ab = 0, a=0 or b=0 x= 2 or 4. --------------------------- b) Solve using the quadratic formula. x= [-b±√(b2 - 4ac)] / 2a in x2 - 6x + 8 = 0, a = 1, b = -6 and c = 8 x = [6±√(36-32)] / 2 x = [6±2]/2 x = 2 or 4 --------------------------- 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. This involves completing the square. y = x2 - 6x + 8 y = x2 - 6x + 9 - 1 y = (x-3)2-1 ---------------------------- b) What is the equation for the line of symmetry for the graph of this function? From part (a), the equation for the line of symmetry is x=h, therefore x = 3 ---------------------------- c) [Graph] It is not necessary to plot points, as you can find the equation of the line of symmetry, the vertex or turning point and intercepts very easily. ---------------------------- d) The graph has the same shape, but is shifted 1 unit down, and 3 units to the right. ---------------------------- 3) You're given the general equation and all the variables, so just pop them in and you get: s = -16t2 + 32t --------------------------- b) Sub in t=1, s = -16(1)2+32(1) = 16ft. --------------------------- c) When it hits the ground, the s = 0. 0 = -16t2 + 32t 0 = t2 - 2t 0 = t(t-2) t = 0 or 2 seconds. Discarding the 0 solution, we get t = 2 seconds. ---------------------------- d) the maximum height is halfway between launch and hitting the ground, at t = 1 second. You can use the answer from b, 16ft. ----------------------------------- 4) The equation for the perimeter is: 2(l+w) = 400ft. l + w = 200ft. l = 200 - w. The equation for the area is A = l x w. sub in (200-w) for l, A = w(200-w) A = - w2 + 200w We have to find the turning (maximum) point. The equation for the line of symmetry is -b/2a = -200/-2 = 100 Therefore at the max, w = 100ft and l = 200-100 = 100ft. The area here is 10,000 ft2.

3x^2 - 6x - 9 = 0
(3x^2 - 6x - 9)/3 = 0/3
x^2 - 2x - 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -2
c = -3

x = [2 ±√(4 + 12)]/2
x = [2 ±√16]/2
x = [2 ±4]/2

x = [2 + 4]/2
x = 6/2
x = 3

x = [2 - 4]/2
x = -2/2
x = -1

∴ x = -1 , 3

no need for the quadratic formula!!

firstly, divide through by 3 to simplify

x^2-2x-3=0

this is easily factorised

(x-3)(x+1)=0

therefore the solutions are x=3 and x=-1

Testing back into the equation, just to check

3(3^2)-6(3)-9=27-18-9=0 (correct)
3((-1)^2)-6(-1)-9=3+6-9=0 (correct)

KISS

you have to do cross factorisation since 3-9=6,

3x -9 l -9x
\ / l
\ / l
/\ l
/ \ l
x +1 l +3x
-------------------------
3x^2 3x -6x


note that you have to be able to get back the terms by multiplying or addition for the x term.

so the answer would be (3x-9)(x+1)=0
3x=9 or x =-1
x=3

it is quite difficult to explain to you ths way, so i suggest you ask someone that can show you on a paper

3x^2 - 6x - 9 = 0

x = -(-6) +/- (square root of) (-6)^2 - (4 x 3 x -9) / 2 x (3)

= 6 +/- (square root of) 36 - ( -108) / 6
= 6 +/- (square root of) 36 + 108 / 6
= 6 +/- (square root of) 144 / 6
= 6 +/- 12 / 6

Therefore x = 18/6 or x = -6/6
= 3 or -1

a=3; b=-6; c=-9

x = [-b +/- √(b^2-4ac)] / 2a
x = [6 +/- √(36-4(3)(-9)]/ 2(3)
x = [6 +/- √144] / 6
x = [6 +/- 12] / 6


x = [6 + 12]/6
x = 18/6
x = 3

x = [6-12]/6
x = -6/6
x = -1

:)

x ² - 2 x + 3 = 0
x = [ 2 ± √ (4 - 12 ) ] / 2
x = [ 2 ± √ (- 8 ) ] / 2
x = [ 2 ± i √8 ] / 2
x = [ 2 ± i 2√2 ] / 2
x = 1 ± i √2

thats a gud explanation....bst of luck