math help please

Question

What is the intermediate step in the form (x+a)2=b as a result of completing the square for the following equation?

6x^2-60x+438

Answer 1

6x²-60x+438 Factor out a 6 from the first 2 terms.

6(x²-10x )+438 Do (b/2)² to find the c term. (-10/2)² = 25

6(x²-10x+25)+438-150 Adding 25 inside the parenthesis is really like adding 6(25)=150 to that side of the equation. To keep the equation in balance, you have to subtract 150 from the other term. Simplify

6(x-5)²+288

Answer 2

6x^2 -60x +438=

(1/6)(x^2 -10x + 73)=

(1/6)(x -10x + 25 + 73) -25/6=

(1/6)(x-5)^2 + 73/6-25/6 =

(1/6)(x-5)^2 +48/6 =

(1/6)(x-5)^2 + 8

basic part of completing the square was taking half of 10 = 5 and squaring it to get 25, then both adding and subtracting 25. Although it's really 25/6 since we factored out 1/6