Question

Solve the quadratic equation by completing the square.
x^2-16x+51=0

Answer 1

Can someone explain it step by step?

Answer 2

Hi...

So, the first step is to isolate the terms which have the x variable. So, subtract 51 from each side.

Answer 3

Can you try that and write what you get?

Answer 4

x^2-16x=-51

Answer 5

Great... now if there were a coefficient (or number) in front of the x^2 term, we would divide both side by that number. In this case the number is (1)... so no need. Understand?

Answer 6

Ok, yes.

Answer 7

Next step, we look at the coefficient of the x-term (-16), we need to take half of it, square it, and then add it to both sides. Can you try that step and let me know what you get?

Answer 8

4^2?

Answer 9

Not quite... half of -16 = -16/2 = -8. Then we would need to square that. (-8)^2 = 64. We would add 64 to both sides.

Make sense?

Answer 10

Oh so we're not trying to get 16?

Answer 11

No, we are trying to complete the square... which is what it means to take the coefficient, halving it and then squaring the result.

Answer 12

so it would look like this?:
(x-8)^2=-64

Answer 13

So, what you will have as a result is:

x^2 - 16x + 64 = -51 + 64

Answer 14

Almost! Just don't forget the first step where we subtracted that 51.

Answer 15

Instead, we'll have:

(x-8)^2 = 13

Answer 16

And of course, we added 64 to each side. <smile>

Answer 17

Can you solve it from there?

Answer 18

x=77 ?

Answer 19

Not quite...


So, to solve, we first take the square root of each side.

x-8 = +/-sqrt(13)
x = 8+sqrt(13) or 8 - sqrt(13).

Answer 20

11.6 and 4.39

Answer 21

well 11.61

Answer 22

@luffingsails Sorry to bother you again but I'm practicing on this problem again and I had a question. How did we get 13 in (x-8)^2=13 ??