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Solve for x in the equation

x^2 + 4x - 4 = 8

Solve for x in the equation x^2 + 4x - 4 = 8-example-1
User Apostofes
by
7.4k points

2 Answers

6 votes

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.

User Alessio Campanelli
by
8.9k points
7 votes
x= -6 or x= 2

Hope this helps
User Andrew Logvinov
by
8.4k points

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