Math Help!!?

Question

Who can help me with this porblem??
the square of 1 more than a number is equal to 4 more than 4 times the number. find the number.

Please help.NEED EXPLANATION!!!!!!!

Thanks!!! I really needed help!!

Answer 1

Let x be the number.

Then (x+1)^2 = 4 + 4x.

(x+1)^2 = x^2 + 2x + 1, so setting that equal to 4 + 4x and moving everything to the left side gives you the equation

x^2 + 2x + 1 - 4 - 4x = 0
or
x^2 - 2x - 3 = 0.

This factors into (x+1)(x-3) = 0, so x = -1 or x = 3. Either value of x works.

Answer 2

we denote the number with the letter x; thus, you have the equation (x+1)^2 = 4+4x . To solve this equation you use the formula (x+y)^2= x^2+2x+y^2; using this the equation becomes x^2+2x+1=4+4x which is equivalent to x^2 +2x+1-4x-4=0 <=> x^2 - 2x - 3 = 0 which is a second degree equation with 2 solutions: x=-1 and x=3; please ask if you need more explanations; it really isn't hard;

Answer 3

Let x be your number. The sentence would translate as:

(x + 1)^2 = 4 + 4x
x^2 + 2x + 1 = 4 + 4x
x^2 - 2x - 3 = 0

Then, you can work it several ways. I like to factor when it's possible:
(x - 3)(x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1

Answer 4

x = 3

(x+1)^2 = 4x+ 4
(x+1) * (x+1) = 4x+4
x+1= 4x+4 / x+1
x+1 = 4(x+1)/(x+1)
x+1 = 4
x = 3

Answer 5

(x+1)^2 = 4x+4
x^2 + 2x + 1 = 4x + 4
x^2 - 2x - 3 = 0
(x-3)(x+1) = 0

So x = 3 or -1

Answer 6

(1+x)^2=4+4x
(1+x)*(1+x)=4+4x
1+x=4+4x
_________
-x -x
__________
1=4+3x
_______
+4 +4
5=3x
_____
3 3

x=1 2/3