solve for x, what is xsquared + 4x + 4 = 7?

The first step would be to try to factor the equation, so you'd want to get all of the terms on the left side of the equation:

x^2 + 4x -3 = 0

Since this won't easily factor, you need to use a different method. I'm sure someone will suggest the quadratic equation, which is fine _if you can remember it_. I much prefer an alternate method, "completing the square," because it's intuitive enough that you can remember how to work out the process even if you forget the steps.

1. Start by moving the constant to the right side of the equation:

x^2 + 4x = 3

2. Then divide the coefficient of x (in this case, 4) by two and square it, adding it to both sides of the equation:

x^2 + 4x + 4 = 7

3. Factor the left side of the equation to (x + a)^2, where 'a' will be the number you just squared:

(x + 2)^2 = 7

4. Take the square root of both sides, remembering that you'll have both a positive and a negative root:

x + 2 = +/- (sqrt)7

5. Move the constant on the left to the right, and you have your two solutions:

x = -2 +/- (sqrt)7

Do you recognise the left side as (x+2) squared? which we write here on Yahoo answers as (x+2)^2

That means x+2 must equal the square root of 7 (about 2.646) or the negative of the square root of 7 (about -2.646). I usually write that here as

x+2 = +or- sqrt(7)

Now by adding -2 to each of those answers, you can get the two values of x

PS You can see that the answers Ferts gave are wrong because when you put x = 1 into x^2 + 4x + 4 you get 9, not 7; and if you put x= -3 you get 1not 7. Her error was that after taking 7 from both sides of the equation and getting

x^2+4x-3 = 0 she thought the expression could be factorised into

(x+3)(x-1), but that gives the middle term as 2x, not 4x.

OK, she corrected it while I was editing mine!! But it's sqrt(7), not 7sqrt(2)

x^2 +4x + 4 = 7

-7 = -7

x^2 + 4x - 3 = 0

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

x = -4 - sqr(4^2 - 4*1 * -3)/2 * 1

4^2 = 16

-4 *1 = -4 * - 3 = 12

16 + 12 = 28

x = -4 + sqr(28)/2

x = -4 - sqr(28)/2

x^2 + 4x + 4 = 7

Subtract 7 from both sides:

x^2 +4x - 3 = 0

Using the quadratic formula:

x = [-4 +- sqr(4^2 - 4(1)(-3))]/2(1)

= [-4 +- sqr(16+12)]/2

= [-4 +- sqr(28)]/2 = [-4 +- sqr(7 x 4)]/2

= [-4 +- 2sqr(7)]/2 = -2 +- sqr(7)

Here are your two values for x

xsquared+4x+4=7 then

x+2squared=7 then

x=-2plus minussquare root of 7

x² + 4x + 4 = 7

x² + 4x - 3 = 0

x = (-4 +/- √16 - 4(1)(-3)) / 2(1)

x = (-4 +/- √28) / 2

x = (-4 +/- 2√7) / 2

x = -2 +/- √7

x^2 + 4x +4 =7

x^2 + 4x -3 = 0

Use quadratic formula;

x =[-4 + or - sqrt( 4^2 -4*1*(-3)]/2

x= [-4 + sqrt(28)]/2

= -2 + sqrt(7)

Also x = -2 -sqrt(7)

x2 + 4x + 4 = 7

is the same as x2 +4x - 3 =0

So applying the formula leads to two answers=

x= (-4+2(squrt of 7))/2

x= (-4-2(squrt of 7))/2

x^2+4x+4=7

x^2+4x-3=0

x=-2 +sqrt[7] or x=-2-sqrt[7]

There are two answers.....x=3 and x=1