Question

Please answer! Thank you

Answer 1

f(x) = (x+14)^2 -202

g(x) = 5(x -3/5)^2 -49/5

Explanation:

Factor out 5 from the expression

g(x) =5(x^2 -6/5x) -8

To complete the square, the same value needs to be added to both sides

g(x) +? =5(x^2 -6/5x +?) - 8

To complete the square

x^2 -6/5+9/25=(x-3/5)^2 add 9/25 to the expression

g(x) + ? = 5 (X^2 -6/5x + 9/25) -8

Since 5(9/25) was added to the right-hand side, also add 5(9/25) to the left-hand side of the equation.

Simplify the answer

g(x)+9/5=5(x-3/5)^2 -8

Move the constant to the right-hand side and change its sign

g(x)=5(x-3/5)^2-8 -9/5

Calculate the diference for the final answer.

Answer 2

(x+30)/(5x+4)

Explanation:

I got this by putting f(x) over g(x), which will give you (x^2+28x−60)/(5x^2−6x−8).

You can simplify this by factoring in both the numerator and denominator:

((x-2)(x+30))/((5x+4)(x-2))

You'll notice that both the numerator and denominator have (x-2) so you can cancel them out.

You'll get (x+30)/(5x+4).