a^2+5a-2=b^2+5b-2

Answer 1

To solve this problem, you must move the terms to one side of the equation, which will make one side equal zero. In this case, we will subtract b^2 to the left side, subtract 5b, and add 2. These terms will now be on the left side of the equation:

a^2+5a-2-b^2-5b+2=0

Within the equation, we then must perform the operation -2+2, which equals zero. We now have a^2+5a-b^2-5b=0

Now, we must use distribute the variables. This uses multiplication:

a(a+5)-b(b+5)=0

Notice that if we multiply this out we have the equation from the previous step. For example (a)*(a) is a^2.

Lastly, it is simple logic that if two numbers, when multiplied, equal zero, then one or both of those terms must be zero.

Therefore, we must take the equation and separate it into two separate equations, like so:

a(a+5)=0 AND -b(b+5)=0

From here, we can further subdivide the equations so that each mini equation is now two:

a= 0 AND (a+5)=0

AS WELL AS

-b=0 AND (b+5)=0

From a=0 and -b=0, we can see that "a" and "b" can both be zero, so both are answers. This leaves us with two remaining equations:

(a+5)=0

AND

(b+5)=0

With this, we do the same process as we did earlier, where we move the terms to one side of the equation. In both cases, we do the opposite of the +5 so that it can be moved to the opposite side of the equation. Thus, we subtract five from both sides:

a=-5

AND

b=-5

Thus, the answers to this problem are a=0 and -5 and b=0 and -5. By plugging the answers back in, we can verify that our answers are correct.