Question

Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

2x2 – 28x + 84 = 0

Answer 1

we need to add "zero" to this equation in order to keep the value the same; we want to change the form of it, and keep the value

Answer 2

first, factor out the 2:

2(x^2 -14x) +84 = 0 ; now we can "complete the square"; which is simply taking half of that "14x" part and (^2)ing it.

14/2 = 7

7^2 = 49 ; lets add 49 inside out paranthesis

2(x^2 -14x+49) +84 - _____ = 0; which means we have to subtract out an equal value now to keep the value the same

Answer 3

2(49) is the extra stuff we included so we have to subtract it out again

2(x^2 -14x+49) +84 - 2(49) = 0 ; rewrite to clean it up

2(x -7)^2 +84 - 98 = 0

2(x -7)^2 -14 = 0 ; now just algebra it into the form they are looking for