slove each equation using the quadratic formula xsquared+6x+9=0?

Answer 1

x^2 + 6x + 9 = 0

A quadratic equation has the form

ax^2 + bx + c = 0

And the quadratic formula is

x = [-b +/- sqrt(b^2 - 4ac)] / (2a)

With a = 1, b = 6, and c = 9, we have

x = [-6 +/- sqrt(6^2 - 4(1)(9))] / 2

x = [-6 +/- sqrt(36 - 36)] / 2
x = [-6 +/- sqrt(0)] / 2

But, sqrt(0) = 0, so we have *one* solution.

x = -6/2 = -3

Answer 2

a) resolve via factorising x2 - 6x + 8 = 0 smash up the 8 into its factors, and then % out 2 which upload to offer -6 and multiply to offer 8. you're able to get -2 and -4. for this reason, (x-2)(x-4) = 0 --- ab = 0, a=0 or b=0 x= 2 or 4. --------------------------- b) resolve utilising the quadratic formulation. x= [-b±?(b2 - 4ac)] / 2a in x2 - 6x + 8 = 0, a = a million, 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, carry out here projects: a) placed the function interior the type y = a(x - h)2 + ok. This is composed of ending up the sq.. y = x2 - 6x + 8 y = x2 - 6x + 9 - a million y = (x-3)2-a million ---------------------------- b) what's the equation for the line of symmetry for the graph of this function? From area (a), the equation for the line of symmetry is x=h, for this reason x = 3 ---------------------------- c) [Graph] that is not any longer mandatory to plot factors, as you will discover the equation of the line of symmetry, the vertex or turning factor and intercepts very particularly. ---------------------------- d) The graph has the comparable shape, yet is shifted a million unit down, and 3 contraptions to the suited. ---------------------------- 3) you're given the time-honored equation and each and all the variables, so basically pop them in and you get: s = -16t2 + 32t --------------------------- b) Sub in t=a million, s = -sixteen(a million)2+32(a million) = 16ft. --------------------------- c) while it hits the floor, the s = 0. 0 = -16t2 + 32t 0 = t2 - 2t 0 = t(t-2) t = 0 or 2 seconds. Discarding the 0 answer, we get t = 2 seconds. ---------------------------- d) the utmost height is midway between launch and hitting the floor, at t = a million 2nd. you need to use the respond from b, 16ft. ----------------------------------- 4) The equation for the fringe is: 2(l+w) = 400ft. l + w = 200ft. l = 200 - w. The equation for the section is A = l x w. sub in (200-w) for l, A = w(200-w) A = - w2 + 200w we'd desire to locate the turning (maximum) factor. The equation for the line of symmetry is -b/2a = -200/-2 = one hundred for this reason on the max, w = 100ft and l = 200-one hundred = 100ft. the section that is 10,000 ft2.

Answer 3

x^2 + 6x + 9 = 0

x = -6 ± sqrt(6^2 - 4(1x9))/2

x = -6 ± sqrt(36 -36)/2

x = (-6 ± 0 )/2

x1 = (-6 + 0)/2 = -3 and x2 = (-6 -0)/2 = -3

Verification

(-3)^2 + 6(-3) + 9 = 0

+9 -18 + 9 = 0

18 -18 = 0

0 = 0

Answer : x = -3

Answer 4

The quadratic formula:
x=-b±√b^2-4ac/2a
a=1,b=6,c=9
x=(-6±√(6)^2-4(1*9))/2(1)
x=(-6±√36-36)/2
x=(-6±√0)/2
x=-6/2
x=-3

Answer 5

-6 + or - the square root of 0 all divided by 2
-6 divided by 2 =-3

Factoring:
(x+3)^2, or -3