Question

Solution of x² + 8x + 12 = 0?

Answer 1

Answer:

x = -6 , -2

Step-by-step explanation:

Find factors of x² and 12, in which, when combined, will give 8x:

x² + 8x + 12 = 0

x               6

x               2

(x + 6)(x + 2) = 0

Check. Use the FOIL method:

First, combine the first terms:  x * x = x²

Next, combine the outside terms: x * 2 = 2x

Then, combine the inside terms: 6 * x = 6x

Finally, combine the last terms: 6 * 2 = 12

Combine like terms: x² + (2x + 6x) + 12

                                  x² + 8x + 12

Solve for the solutions. Set each parenthesis equal to 0:

(x + 6)(x + 2) = 0

(x + 6) = 0

(x + 2) = 0

Isolate the variable x. Subtract 6 & 2 from both sides for their respective equation:

x + 6 = 0

x + 6 (-6) = 0 (-6)

x = 0 - 6

x = -6

x + 2 = 0

x + 2 (-2) = 0 (-2)

x = 0 - 2

x = -2

x = -6 , -2

~

Answer 2

Answer: {-6, -2}

Step-by-step explanation: First look if you can factor the left side.

In this case, the trinomial on the left can be factored.

The left side of the equation is a trinomial in a special form

that can be factored as the product of two binomials.

As our first term for each binomial, we will have the factors of x².

Since x² breaks down into x · x, we use an

x in the first position of each binomial.

For our second term, we are looking

for factors of 12 that add to 8.

In this case, these factors are 6 and 2.

So we have (x + 6)(x + 2) = 0.

So either x + 6 = 0 or x + 2 = 0.

Solving each equation from here, we find that x = -6 or x = -2.

We can write our answer as the solution set {-6, -2}.