Sat math question
f(x) = x^2 - 2x + 8
g(x) = -x^2 +18x +4
the two functions defined above are equal to each other when x=5+a or x=5-a, where a is a constant. what is the value of a?

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Step-by-step explanation:

So we are given the equations are equal for .

If the functions are equal for those values then their difference is zero for those values:

Combine like terms; keep in mind we are subtracting over the parenthesis:

Since all terms have a common factor of 2, then divide both sides by 2:

When compared to we should see:

Now use quadratic formula.

Plug in the values we found:

Let's simplify:

92 isn't a perfect square but contains a factor that is; 92=4(23):

Divide top and bottom by since all three terms have a common factor 2:

So f and g are equal for:

When compared to we see that .

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