two negative integers are 8 units apart on the number line and have a product of 308. which equation could…

two negative integers are 8 units apart on the number line and have a product of 308. which equation could be used to determine x, the smaller negative integer?\n$x^{2}+8x - 308 = 0$\n$x^{2}-8x + 308 = 0$\n$x^{2}+8x + 308 = 0$\n$x^{2}-8x - 308 = 0$

two negative integers are 8 units apart on the number line and have a product of 308. which equation could be used to determine x, the smaller negative integer?\n$x^{2}+8x - 308 = 0$\n$x^{2}-8x + 308 = 0$\n$x^{2}+8x + 308 = 0$\n$x^{2}-8x - 308 = 0$

Answer

Explanation:

Step1: Define the larger integer

If the smaller negative - integer is (x), and the two negative integers are 8 units apart on the number line, then the larger negative integer is (x + 8).

Step2: Set up the product equation

Since their product is 308, we have (x(x + 8)=308).

Step3: Expand the left - hand side

Expand (x(x + 8)) using the distributive property (a(b + c)=ab+ac). Here, (a = x), (b=x), and (c = 8), so (x(x + 8)=x^{2}+8x). The equation becomes (x^{2}+8x=308).

Step4: Rearrange the equation to standard form

Subtract 308 from both sides of the equation (x^{2}+8x = 308) to get (x^{2}+8x-308 = 0).

Answer:

A. (x^{2}+8x - 308=0)