Question

Solve x2 + 4x − 4 = 0.

Answer 1

Is the picture relevant?

0 = x^2 + 4x - 4

We know numbers that multiply to -4 are:
4 -1 , -4 1
2 -2 , -2, 2
We know that none of these sum to +4
So it cannot be a ()()

It must be = (x+2)^2 - 8
I jumped ahead cause I really couldn't be bothered explaining more.

Answer 2

For this, you can use the quadratic formula.
-b+_(b^2-4ac)^0.5
x= ----------------------------
2a

Now we get the variables a, b, and c from this equation:
Ax^2+bx+c=0
Now if you want an explanation of how that equation works, I will derive and explain it for you if you let me know you want me too.


x^2+4x-4=0
Ax^2+bx+c=0
So the variables a,b, and c stand for the coefficients infringed of each x.
So if we combine the two equations, we find that:
a=1
b=4
c=-4

Now that we have only one unknown variable (aka variable (x)), we can substitute the numbers into the quadratic equation.

-4+_(4^2-4*1*(-4))^0.5
x= ----------------------------------
(2*1)

x=-4+_(16+16)^0.5
----------------------
2

x=-4+_(32)^0.5
----------------------
2

x=-4+_4(2)^0.5
----------------------
2
x=-2+_2(2)^0.5

This is your answer. If you have any questions, feel free to ask. I'll try to stay on as long as I can. I know these problems a fairly to grasp.