I need a bit of algebra help?

Question

whats is x if x squared plus 2x equals 4?

Answer 1

x^2 +2x=4

x^2+2x-4=0

by using a scientific calculator...

x=1.236 or x= -3.236

Answer 2

x^2 + 2x = 4, then x^2 + 2x + 1 = 5 so (x+1)^2 = 5

and x+1 = rt5 or - rt5 so x = -1 + rt5 or -1 - rt5.

Answer 3

1x2 +2x=4

3x2=4

x= 1 and one fourth (square root over x and 1 and one fourth).

Answer 4

Okay so the problem you have is:

x^2 + 2x = 4

In order to solve this problem, you must complete the square.  In order to do this you take the b term (meaning ax^2+bx+c) which in this case is 2, you take (b/2)^2, so (2/2)^2, so 1. Now you must add 1 to both sides of the equation.  If you do to one side (add/subtract/etc), so you then have x^2+2x+1 = 5.  This is the same as one of the answers above.  Now, you want to factor this equation, into squares, hence completing the square.  The equation then becomes (x+1)^2 = 5.  Check by the FOIL (expanding the equation, first, outside, inside,last) if you would like.

(x+1)(x+1)

1. first is x*x = x^2, outside x*1 = x, inside 1*x = x, last, 1*1 = 1

2. Combine: x^2 + 2x + 1 = 5, does this check, yes, so it is (x+1)^2 = 5

Now in order to remove the square on the left side of the above equation, we must take the square root of both sides (what you do to one side of the equation, you must do to both)

SQRT ((x+1)^2) = SQRT (5)

The root of a square is whatever was being squared, in this case, (x+1)

So (x+1) = SQRT (5)

Subtract 1 from both sides and you get x = SQRT (5) - 1

Now, you will see some people have shown both positive and negative roots of five, this is because when you multiple two same positives (square) or two negatives, its always a postive resultant, therefore the square root can be positive or negative.



The answer is +/- (SQRT(5) - 1)