Complete the square?

Question

2x^2-8x+16=0

Answer 1

doesn't have real solutions but..

2x^2 - 8x + 16 = 0

Get rid of the lead term's coefficient by dividing everything by 2
x^2 - 4x + 8 = 0

Take 8 over to the right
x^2 - 4x = -8

Add half the linear term squared to both sides (in this case 4) to both sides to complete the square on the left
x^2 - 4x + 4 = -8 + 4
x^2 - 4x + 4 = -4

Factor left
(x-2)^2 = -4

Take the square root of both sides and note that these solutions are not real.
x-2 = ± √-4
x = 2 ± √-4
x = 2 ± √-1 √4
x = 2 ± 2i

Answer 2

A little background first
a^2 +2ab +b^2 =(a+b)^2
x^2 -6x+9 =(x-3)^2
If you do enough of these, you can see that the last term is half the middle term squared. And that's the secret to completing the square.WARNING! The coefficient of the square term must be +1 before you start the complete the square process.
For your equation, I see that the coefficient of the x^2 term isn't +1, so I must make it so
2x^2-8x+16=0
Divide all terms by 2
2x^2/2 -8x/2 +16/2=0/2
x^2-4x+8=0
Now I'm ready.
A.) Move the constant term to the other side of the equation. x^2 -4x=-8
B.)Take half the x term's coefficient and square it
(-4)/2 squared=(-2)(-2)=4
C.)Add it to BOTH sides of your equation. (if you added it to only one side, you would destroy the original equality of the equation)
x^2-4x+4=-8+4
D.)Tidy up
(x-2)^2=-4
You have "completed the square.

I think I know where this is heading. All quadratic equations can be written in the form ax^2+bx+c=0
Your teacher is going to use the "complete the square" process on ax^2+bx+c to get a formula for solving what x is. If you can complete the square, you will be able to follow the derivation of the formula.
Good luck with your math work.

Answer 3

Hey there!

Here's the answer.

2x^2-8x+16=0 --> Write the problem.
x^2-4x+8=0 --> Divide 2 on both sides of the equation.
x^2-4x=-8 --> Subtract 8 on both sides of the equation.
x^2-4x+(4/2)^2=-8+(4/2)^2 --> Add (4/2)^2 on both sides of the equation, by the definition of completing the square.
x^2-4x+4=-8+4 --> Replace (4/2)^2 with 4.
x^2-4x+4=-4 --> Add -8 and 4.
(x-2)^2=-4 --> Factor out x^2-4x+4.
x-2=±sqrt(-4) --> Take the square root on both sides of the equation.
x-2=±sqrt(4*-1) --> Rewrite -4 as 4*-1.
x-2=±sqrt(4)*sqrt(-1) --> Use the formula sqrt(ab)=sqrt(a)*sqrt(b).
x-2=±2sqrt(-1) --> Replace sqrt(4) with 2.
x-2=±2i --> Use the fact that i=sqrt(-1).
x=2±2i Add 2 to both sides of the equation.

So the solutions are x=2-2i and x=2+2i.

Hope it helps!

Answer 4

x² - 4x + 8 = 0
(x² - 4x + 4) - 4 + 8 = 0
(x - 2)² = - 4
(x - 2) = ± 2i
x = 2 ± 2i
x = 2(1 ± i)