Question

I need help to Solve 2x2 - 8x = -7.my choices are.

negative 2 plus or minus square root of 2

negative 2 plus or minus 2 square root of 2

quantity of 2 plus or minus square root of 2 all over 2

2 plus or minus square root of 2 end root over 2

Answer 1

By 2x2, do you mean \[2x ^{2}\]

Answer 2

If so, then this is how I did it.

1) First, get that -7 over to the left side to make it a nice quadratic formula like so:
\[2x ^{2} -8x +7 = 0\]

2) Now, if we try to factor this, it doesn't come out nice. So, if we can't flat out factor it, what's another method we can use to make a formula factor-able?

Answer 3

yes

Answer 4

(Hint: what can we COMPLETE to make this quadratic SQUARED formula factor-able?)

Answer 5

I cant remember

Answer 6

Complete the...

Answer 7

square

Answer 8

Ok, so, what's the formula for completing the square?

Answer 9

i dont know my teacher doesn't explain anything.

Answer 10

Ok, well, the formula for completing the square is: \[\frac{ b }{ 2a }\]

with, \[ax ^{2} + bx + c = 0\]

So, what's A and B?

Answer 11

I should mention that A, B, and C are all constants, not just separate variables themselves.

Answer 12

2 and 8

Answer 13

Good, but we have an issue. The way this is currently worded has that pesky 2 out in front. That's no good! We need a formula like the following: \[a(x + d)^{2} + e = 0\]
With \[d = \frac{ b }{ 2a }\]
and
\[e = c - \frac{ b ^{2} }{ 4a }\]

So, what can we do to the formula to make \[2x ^{2} -8x+7=0\]
look like:
\[ax ^{2}+bx+c\]
?

Answer 14

okay i got lost

Answer 15

Im starting to think its the third one after looking at it for a long time

Answer 16

I'll go ahead and continue, but try to work that out before looking ahead.

To get it in proper format, we can divide everything by two, which leads us to:
\[x ^{2}-4x+\frac{ 7 }{ 2 }=0\]

Now we do completing the square, which leads to:
\[(x-2)^{2} - \frac{ 1 }{ 2 } = 0\]
Now, just some simple simplification.

1) \[(x-2)^{2} = -\frac{ 1 }{ 2 }\]
2) \[(x-2)=\sqrt{\frac{ 1 }{ 2 }}\] or \[(x-2)=-\sqrt{\frac{ 1 }{ 2 }}\]
3) \[x=2-\sqrt{\frac{ 1 }{ 2 }}\] or \[x=2+\sqrt{\frac{ 1 }{ 2 }}\]

Answer 17

Oops! Had an arithmatic error in there. Before 1), I meant to move the - 1/2 to the right side.

Answer 18

Did that make sense? If not, say so, and I'll find another way to explain it.

Answer 19

i understand it now once i see the numbers

Answer 20

Sorry, I know that seemed a bit confusing, but I promise, it's not as bad as it seems.