# Zero Factor Property

First problem is “x2 + 7x + 12 = 0”. I will solve this by factoring. So, I begin by finding two numbers that multiply to make 12 but add together to make 7. The first set of numbers that come to mind are 3,4.

(x + 3)(x + 4)= 0

Then I apply the Zero Factor Property to set them equal to zero.

(x + 3)= 0

(x + 4)= 0

After that I solve for “x” by subtracting 3,4 from each side.

x = -3,-4

If I were to solve this “x2 + 7x + 12 = 0” by completing the square it would take a little longer.

First I would keep the “x” terms on the left side

x2 + 7x = -12

Next I will take half of 7 and square it.

[7 * ½]2 = 49/4

49/4 has to be added to both sides

x2 + 7x + 49/4 = -12 + 49/4

After simplifying and taking the sqrt of both sides it becomes x + 7/2 =± sqrt ¼

Now I solve for “x”

x = – 7/2 ± ½

Which becomes –3,-4

Second problem “4×2 – 12x + 9 = 0” is I will solve using the quadratic formula. I’m not that skilled in using word so I will just explain the process of solving using the quadratic formula. Below I have the problem and the formula.

4×2 – 12x + 9 = 0

First, I began by plugging in my equation, into the formula. -12 will turn into positive then ± sqrt of 12 squared minus 4 (4)(9) over 2(4). After solving I got 12 ± sqrt of 0 over 8. The discriminant is 0, so that means there is no real root. Finally, 12/8 simplifies to 3/2 or 1.5

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