Solve x2 + 6x = 7 by completing the square. which is the solution set of the equation? {–7, 1} (negative 3 minus startroot 10 endroot comma negative 3 + startroot 10 endroot) (3 minus startroot 10 endroot comma negative 3 + startroot 10 endroot) {1, 7}

The two solutions are x = -7 and x = 1

Step-by-step explanation:

We complete the square for the expression on the left of the equal sign, by adding the "square of half of the coefficient of the term in x". That is, in our case we need to add  

So we proceed to add 9 on both sides of the equation, that way completing a perfect square trinomial on the left side of the equal sign:

Notice now that the perfect square on the left is , so we replace it in our equation:

Therefore, we get two possible solutions:

a) , and

b)

So our two solutions are x= -7 and x=1

answer: true

step-by-step explanation:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}