can you help me finish off this equation?

Question

solve : x^ - x - 20 = 0

i have:
(x - 5) (x +4)
x - 5 = 0 or x + 4 = 0
so x =5 or x = -4

use your results to solve:
(2t + 2/t) ^ - (2t + 2/t) - 20 = 0

i have:
2t + 2/t = -4 or 2t + 2/t = 5
2t^ + 2 + 4t = 0 or _________
2t^ + 4t + 2 = 0 or 2t^ - 5t + 2= 0
(t ) (t ) =0 or (t ) (t )


can someone tell me where i'm going wrong and help me fill in the blanks plz? thanks! :)

EDIT
the (t) 's
should be (t___)

Answer 1

You are correct

x² - x - 20 = 0

The middle term is - x

The first term x² = 1

Find the sum of the middle term

Multiply the first term 1 times the last term - 20 and factor

Factors of - 20

1 x - 20
2 x - 10
4 x - 5. . .←. .use these factors

- 5 and + 4 satisfy the sum of the middle term

insert - 5x and + 4x into the equation

x² - x - 20 = 0

x² - 5x + 4x - 20 = 0

Group factor

(x² - 5x) + (4x - 20) = 0

x(x - 5) + 4(x - 5) = 0

(x + 4)(x - 5) = 0

- - - - - -

Roots

x + 4 = 0

Transpose 4

x + 4 - 4 = 0 - 4

Collect like terms

x = - 4
- - - - - - -

Roots

x - 5 = 0

Transpose 5

x - 5 + 5 = 0 + 5

Collect like terms

x = 5
- - - - - - - -s-

Answer 2

You just stopped to soon!
(2t + 2/t) ^ - (2t + 2/t) - 20 = 0
2t + 2/t = -4 or 2t + 2/t = 5
2t^ + 4t + 2 = 0 or 2t^ - 5t + 2= 0
now finish each problem using factoring
(2t+2)(t+1)=0 (2t-1)(t-2)=0
t=-1 t= 1/2 t=2

Answer 3

okay firstly your first part of x=5 or -4 is correct.

Second part if you let x=2t+2/t
they your equation:
(2t + 2/t) ^ 2- (2t + 2/t) - 20 = 0
is exactly the same as the first one
so the solutions of x= 5 or -4
becomes

2t+2/t= 5 or 2t+2/t=-4
this can be rearranged so that
2t^2+2=5t or 2t^2+2=-4t
so you then get
2t^2-5t+2=0 or 2t^2+4t+2=0
so we have
2t^2-5t+2=0 or t^2+2t+1=0
(2t -1)(t -2) or (t+1)^2
t=1/2 or 2 or t=-1

Answer 4

whoa! what level math is this? first part makes sense, second, not so much! lol

Answer 5

im only in year 8 lol