Solve x 2 - 4x - 7 = 0 by completing the square. what are the solutions?

x = 2±sqrt(11)

Step-by-step explanation:

x^2 -4x - 7 =0

Add 7 to each side

x^2 -4x -7+7 =0+7

x^2 -4x =7

To complete the square take the coefficient of the x term and  divide by 2 and then square it.  Add it to both sides

-4 /2 = -2 then square

(-2)^2 = 4

Add 4 to both sides

x^2 -4x+4 =7+4

x^2 -4x+4 = 11

Factor the left side into (x-b/2)^2

(x-2)^2 =11

Take the square root of each side

sqrt((x-2)^2) =±sqrt(11)

x-2 = ±sqrt(11)

Add to to each side

x-2+2 = 2±sqrt(11)

x = 2±sqrt(11)

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step-by-step explanation:

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages