Solve for x in the equation x2+4x-4=8

Given the numerical equation:

x^2 + 4x - 4 = 8

Solve for x.

Solution:
In order to solve for x, we first transpose 8 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

x^2 + 4x - 4 - 8 = 0

x^2 + 4x - 12 = 0

In order to solve for the roots or zeros of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 4, and when multiplied, the answer is -12. Hence, if we are unable to find the number, we will use the quadratic formula. In our case, the factors that satisfy the given equation are, 

( x + 6 ) ( x - 2 )

To check if the factors are true, we simply apply the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.

To clearly see how it works, here's a step by step solution.

= (x)(x)
=x^2
First term of the first equation multiplied to the first term of the second equation.

=(x)(-12)
= -2x
First term of the first equation multiplied to the last term of the second equation.

=(6)(x)
=6x
Last term of the first equation multiplied to the first term of the second equation.

=(6)(-2)
= -12
Last term of the first equation multiplied to the fast term of the second equation.

= x^2 - 2x + 6x - 12

= x^2 + 4x - 12

Now that we've proven that the factors are true, we need to equate the factors to 0.

x + 6 = 0

x - 2 = 0

Transpose 6 and -2 to the other side of the equation.

x = -6

x = 2

Final answer:

x = -6

x = 2