Answer:
x = -6 or x = 2
Explanation:
Step 1: Put the equation in standard form:
First, we need to subtract 8 from both sides to put the equation in the standard form of a quadratic, whose general equation is given by:
ax^2 + bx + c = 0
(x^2 + 4x - 4 = 8) - 8
x^2 + 4x - 12 = 0
Step 2: Factor the equation:
In our equation, 1 is a, 4 is b, and -12 is c.
Thus, we can factor the equation by finding two terms whose product is equal to a * c and whose sum equals 4.
We see that 2 * -6 = -12, which is the same as 1 * -12 = -12.
Furthermore, 2 - 6 = 4.
To plug in 2 and -6 as a factor, we use the opposite sign of 2 and -6.
Thus, the factored form of the equation is:
(x - 2)(x + 6) = 0
Step 3: Solve for x by setting each term equal to 0:
We can solve for x by setting (x + 2) and (x - 6) equal to 0:
Setting (x - 2) equal to 0:
(x - 2 = 0) + 2
x = 2
Thus, one solution for x is x = 2.
Setting (x + 6) equal to 0:
(x + 6 = 0) - 6
x = -6
Thus, the other solution for x is x = -6.
Thus, our solutions are x = 2 and x = -6.
Optional Step 4: Check validity of solutions:
We can check that our answers for x are correct by plugging in 2 and -6 for x in the original equation and seeing if we get 8:
Checking x = 2:
(2)^2 + 4(2) - 4 = 8
4 + 8 - 4 = 8
12 - 4 = 8
8 = 8
Checking x = -6:
(-6)^2 + 4(-6) - 4 = 8
36 - 24 - 4 = 8
12 - 4 = 8
8 = 8
Thus, our answers for x are correct.