For all you math experts?

Question

1. Solve (x - 3 )^2 - 49 =0 where x is a real number. Simplify your answer as much as possible.


2. Solve w^2 = 14 where w is a real number, simplify your answer as much as possible.

Thank you

Answer 1

The easiest way to solve this is:

(x - 3)^2 = 49
x - 3 = +/- 7
x - 3 = 7 or x - 3 = -7
x = 10 or x = -4

You could multiply it out, subtract the 49 and refactor it, but you'll get the same answer.

x^2 - 6x + 9 - 49 = 0
x^2 - 6x - 40 = 0
(x - 10)(x + 4)



w^2 = 14
w = +/- sqrt(14)
w = +/- 3.74

There really isn't any way to simplify it.

Answer 2

(x-3)^2 - 49 = 0
(x - 3)^2 = 49 solving square root
(x - 3) = 7 then
x = 7 + 3
x = 10

Answer 3

(x - 3 )^2 - 49 =0
(x - 3 )^2 = 49
(x - 3 )=+7 or -7
x=7+3 or -7+3
x=10 or -4

w = 14^ (1/2)

w = 1/2 * (Ans + 14/Ans)
let Ans 1 = 3

w = 1/2 * (3 + 14/3) = 3.8333
w = 1/2 * (3.8333 + 14/3.8333) = 3.7428

continue until you get + or - 3.7416573867739413855837487323165!!!!

Answer 4

1) Here is the best way to solve this problem
x^2 - 6x + 9 - 49 = 0
x^2 - 6x - 40 = 0
(x - 10)(x + 4)


2)Here you go
w^2 = 14
w = +/- 3.74

Answer 5

1. (x -3)^2 - 49 = 0

(x-3)^2 = 49

sqrt (x-3)^2= sqrt(49)

x -3 = 7

x=4

2. w^2 =14

sqrt(w^2) = sqrt(14)

w = sqrt(14)

w = sqrt(2) * sqrt(7)

Answer 6

1) Use the formula for factoring the difference of two squares, or even easier, move the 49 and take square roots.
2) Take the square root of both sides, ignoring the negative root since they specify that w is real.

Answer 7

1, x=8 or X= -5
2, 14^0.5