Question

5. Solve for x: 2x2 - 4x - 14 = 0 (completing the square)

Answer 1

1-2squ 2 and 1+2squ2

Answer 2

So far I have 2x^2 - 4 = 14
That can be factored so I get 2 (x^2 - 2x) = 14
Now i make my perfect square by dividing -2 by 2 and squaring that answer.
Now I get 2 ( x^2 - 2x + 1) = 14
Then I factor it and get 2 (x - 1)^2 = 14
Now what do I do next?

Answer 3

Then do I figure x - 1 = 7 to solve for x?

Answer 4

wait... there's a problem... here: 2( x^2 - 2x + 1) = 14

Answer 5

When I try to figure it out I keep getting x = 1, then I check it and its wrong. :(

Answer 6

since you added 1 to the left side to make that perfect square trinomial, you actually added 2 to the left side. you must also add 2 to the right side.

Answer 7

Divide each term by 2 to get:

x² - 2x - 7 = 0

Complete the squares..

x² - 2x + c = 7 + c
x² - 2x + 1 = 7 + 1
(x - 1)² = 8

Square root property:

√(x - 1)² = ±√8
x - 1 = ±2√2

Hence, by adding both sides by 1, we obtain x = 1 ± 2√2

Answer 8

but to make things simpler, i'd start out first by dividing the whole equation by 2 so i'd be working with \(\large x^2-2x-7=0 \) instead...

Answer 9

^^^ that's it.... @jessica52595 did it for you.

Answer 10

Thank you! @ByteMe and @jessica52595

Answer 11

yw...:)