Do I have the right answer to this math question?

Question

If x(2) + x =20, what are the values for x that will make the equation true? My book states that answer 1 is correct, I think my book is wrong and I have the right answer the GED book gives these possible choices
(1.) -5 and 4 (book claims this is the right answer)
(2.) -5 and -4
(3.) 5 and 4
(4.) 5 and -4
(5.) Not enough information is given

I think the answer would be 25 and -5 in order = 20
Am I correct and is the book wrong? Please help me. This is driving me nuts.

x(^) my bad not x(2)

Answer 1

Assuming you mean X-squared for "x(2)" (which is usually written as "x^2" here), then both x=-5 and x=4 are solutions to the equation.

(1) x = -5:

x^2 + x = 20
(-5)^2 + (-5) = 20
25 - 5 = 20
20 = 20

(2) x = 4:

x^2 + x = 20
4^2 + 4 = 20
16 + 4 = 20
20 = 20

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You can solve the quadratic to prove what the roots are:

x^2 + x = 20
x^2 + x - 20 = 0

If you can't factor that into (x + 5)(x - 4), then use the quadratic formula:

x = (-1 +/- sqrt(1^2 - 4*1*(-20)))/(2*1)
x = (-1 +/- sqrt(1 +80))/2
x = (-1 +/- 9)/2

Two solutions:
x = (-1 + 9)/2 = 8/2 = 4
x = (-1 - 9)/2 = -10/2 = -5

Answer 2

The book is correct. Move the 20 to the left side of the equation and change its sign. You can move any term to the other side of the equation if you just change its sign. Now you get x^2+x-20=0, Factoring it, you get (x+ 5)(x-4)=0. What would it take to make each of the factors become zero? (-5+5)(4+-4). The two answers are -5 and 4.

Answer 3

x(2) + x =20
2x + x = 20
3x = 20

it's (5.) not enough info given

nvm i think you meant x^2 + x = 20
then it would be 5 and -4 which is answer choice (1.)
(x+5)(x-4)
(-5+5)(4+-4)


LOL

Answer 4

x^2+x=20
x^2+x-20= 0 /use pq formula p=1 and q=-20
x= -0.5+(20.25)^0.5 and -0.5-(20.25)^0.5
First solution is -0.5+4.5 = 4
Second solution is -0.5 - 4.5 = -5
Answer 1 is correct