Question

FAST PLSSSSS

Find all real solutions to

x^2 + 4x + 4 = 100x^2 + 20x + 1.

If you find more than one, then list the values separated by commas.

Answer 1

1/9, (-3)/11

Explanation:

Both the left and right side are perfect squares,

(x + 2)^2 = (10x + 1)^2

In order for the squares to be equal, we must have the inner expressions equal to each other or negations of each other:

(x + 2) =
`\pm` (10x + 1)

or

x + 2 = -10x - 1

Simplifying the first equation gives 9x = 1 so 1/9 and simplifying the second equation gives 11x = -3, so (-3)/11

Answer 2

factor:

x^2+2x+2x+4

x(x+2)+2(x+2)

(x+2)(x+2)

100x^2+20x+1

100x^2+10x+(10x+1)

10(10x+1)+(10x+1)

(10x+1)(10x+1)=(x+2)(x+2)

Hope this helps you