Flamo:
Solve the system y = -x + 7 and y = 0.5(x - 3)2
Hero:
@Flamo multiply both sides of y = -x + 7 by 2.
Flamo:
2y = -2x + 14
Hero:
Next, multiply both sides of \(y = 0.5(x - 3)^2\) by 2.
Flamo:
2y = 1(2x - 6)^2?
Hero:
More like \(2y = 1(x - 3)^2\)
Flamo:
Oh.
Hero:
Next you set both expressions for 2y equal to each other.
Flamo:
Hmm..
Flamo:
I have this written down. y = -x + 7 and y = 0.5(x - 3)^2 0.5(x - 3)^2 = -x + 7 Multiply Both sides by 2 -2x + 14 = x^2 - 6x + 9
Flamo:
So that's incorrect?
Hero:
It's the exact same thing actually.
Flamo:
Oh, So what do you need to do *from there*?
Hero:
Solve for x, which is what we were doing previously.
Flamo:
Oh
Hero:
I was trying to show you how to do it but once again, you have introduced something else which is adding to your confusion.
Flamo:
I did? Oh...
Flamo:
The Teacher says, After -2x + 14 = x^2 - 6x + 9 <---- You need to Simplify: x^2 - 4x - 5 = 0 then factor to figure out the x's, then sub it x's to get y
Hero:
Yeah, see you did it again. I was showing you how to do it, then you interrupt by introducing "what the teacher said". I don't care what the teacher said.
Flamo:
Oh, You said Solve for x. Right?
Flamo:
No no no no, You said: Next you set both expressions for 2y equal to each other.
Flamo:
Right?
Hero:
Yes, I did and then you proceeded to post what your teacher said.
Flamo:
Oh, Sorry. I was Confused. Let's Continue from there then.
Hero:
Okay, still waiting for you to set the expressions for 2y equal to each other.
Flamo:
Yeah, i'm doing that right now.
Flamo:
2y = -2x + 14 and 2y = 1(x - 3)^2
Flamo:
Right?
Hero:
Yes, and so since we know 2y = 2y, then what expressions are equal to each other?
Flamo:
Uhh, I don't know.. ;-;
Hero:
\(2y = 2y\) means that \(-2x + 14 = (x - 3)^2\)
Flamo:
OH
Hero:
2y = -2x + 14 || || 2y = 1(x - 3)^2
Flamo:
So You Subtract?
Hero:
"Wondering how @flamo concluded that equal signs mean subtract".
Flamo:
Oh... They were Sideways, Didn't realize that they were equal Signs...
Flamo:
My bad... ;-;
Flamo:
Okay, the equations are equal, now what? ;-;
Hero:
You have to post your steps here.
Flamo:
y = -x + 7 and y = 0.5(x - 3)^2 0.5(x - 3)^2 = -x + 7 Multiply Both sides by 2 2y = -2x + 14 and 2y = 1(x - 3)^2 2y = -2x + 14 = 2y = 1(x - 3)^2
Flamo:
That's the steps I've written when we were solving the problem
Hero:
It's true what you've written except since we need to solve for \(x\) you only include the expressions with \(x\)
Flamo:
Oh? So You take the 2y out on Both equations?
Hero:
Yes
Flamo:
-2x + 14 = 1(x - 3)^2? Sorry I had to do something, ;-;
Flamo:
@Hero
Hero:
Finally.... Now question. what is \(1 \times 7 = \)
Flamo:
7
Hero:
Good so \(1 \times (x - 3)^2\) =
Flamo:
...
Flamo:
Oh.
Flamo:
Uhh (x - 3)^2
Hero:
Correct. So basically what we have is \(-2x + 14 = (x - 3)^2\)
Hero:
And we can expand \((x - 3)^2\) using (not FOIL) but distributive property
Flamo:
Oh
Flamo:
So (x - 3) - (3 - x)?
Hero:
No \((x - 3)^2\) means multiply \((x - 3)\) by itself twice.
Flamo:
Oh... I feel Dumb. ;-; \[(x - 3) \times (x - 3)\]
Flamo:
Which is \[x^2 - 6x +9 \] Right @Hero?
Hero:
Correct
Flamo:
y = -x + 7 and y = 0.5(x - 3)^2 0.5(x - 3)^2 = -x + 7 Multiply Both sides by 2 2y = -2x + 14 and 2y = 1(x - 3)^2 -2x + 14 = 1(x - 3)^2 -2x + 14 = (x - 3)^2 -2x + 14 = (x - 3) * (x - 3) -2 + 14 = x^2 - 6x + 9
Flamo:
This is what I have so Far. Correct?
Flamo:
@Hero
Hero:
Looks good
Flamo:
Okay, So now what?
Flamo:
From this: -2 + 14 = x^2 - 6x + 9
Hero:
Actually the x is missing from 2.
Flamo:
Oops
Flamo:
From this: -2x + 14 = x^2 - 6x + 9
Hero:
Next subtract 14 from both sides. Then add 2x to both sides.
Flamo:
\[-2x = x^2 - 6x + (-5)\]
Flamo:
Okay, I subtracted 14 from both Sides, now add 2x?
Flamo:
Or Subtract *-2x*?
Flamo:
From Both sides.
Hero:
It's exactly like I suggested above.
Flamo:
Oh, So \[x^2 - 4x + (-5)\]
Flamo:
Okay, So I added 2x to both sides.
Hero:
Yeah but you still need to put something on the other side of the equal sign.
Flamo:
0?
Flamo:
0 = x^2 - 4x + (-5)?
Hero:
Yes correct
Flamo:
Oh, Okay. Now what?
Hero:
You can re-write the expression above as \(0 = x^2 - 4x - 5\) since \(a + (-b) = a - b\)
Flamo:
Oh, Okay
Flamo:
Okay, I did that, Now what?
Flamo:
\[0 = x^2 - 4x + 5\]
Hero:
You wrote the equation I wrote above incorrectly.
Flamo:
Oh.. ;-;
Flamo:
\[0 = x^2 - 4x - 5\]
Flamo:
Okay, now what?
Hero:
Now you factor \(x^2 - 4x - 5\)
Flamo:
(x - 5) (x + 1)
Hero:
Yeah, but what are your steps to get that?
Flamo:
AC Method?
Hero:
When I ask "What are your steps?", that implies for you to actually post those steps.
Flamo:
Oh, I used a Calculator, ;-;
Flamo:
Oh, I used a Calculator. ;-;
Hero:
Okay, I'm about to go take a nap.
Flamo:
...
Flamo:
;-;
Flamo:
I can't stop you... ;/
Hero:
You have to learn how to factor quadratic expressions. It takes too much time to teach. Review some of the other threads where I've shown other users how. I know you've been watching. Don't pretend you haven't.
Flamo:
Yes, I have been watching.
Hero:
We have to find two numbers \(m\) and \(n\) such that \(m + n = |b|\) \(m \times n = ac\) We need to find that so that we can input \(m + n\) here in place of \(b\) \(x^2 -(m + n)x - 5\) Obviously \(m + n = 4\) in this case.
Flamo:
\[x^2 - (4)x - 5\]
Flamo:
Or Just 4x
Hero:
Yes we know that already, but it doesn't get us any closer in terms of factoring. We have to "split the middle term"
Flamo:
2 + 2?
Flamo:
= 4?
Flamo:
2 + 2 are the middle Terms for M and n
Hero:
No, \(m \times n\) has to equal -5
Hero:
\(m + n\) has to equal \(4\)
Flamo:
Oh
Flamo:
(m + n) = 4 So m = 2 as well as n. So (2+2) = 4.
Hero:
\(m\) and \(n\) has to satisfy both requirements. How about \(5 - 1 = 4\) \((5)(-1) =-5\)
Hero:
So looks like it's going to be \(m = 5\) and \(n = -1\)
Flamo:
Oh.
Flamo:
\[x^2 - 5 + (-1) - 5\]?
Flamo:
Or do You not put it in the equation?
Hero:
You forgot the x. It's \(x^2 -(5 - 1)x - 5\)
Flamo:
Oh..
Hero:
And the whole time, the expression should be set equal to zero.
Flamo:
Oh
Flamo:
\[0 = x^2 - (5 - 1)x - 5\]?
Hero:
Yes, now you have to distribute the negative and the x within the parentheses.
Flamo:
Oh.. Hm..
Flamo:
I don't get it.. Sorry ;-;
Hero:
Well, I'm going to take a nap. Review the tutorials.
Flamo:
Okay. Have fun... ;-;
Flamo:
I suck.. ;/
Flamo:
...
Flamo:
x^2 - 4x - 5
Flamo:
x^2 = x * x
Flamo:
(x )(x )
Flamo:
-5 = - 5
Flamo:
(x - 5)(x - 1)
Flamo:
):
Flamo:
(x - 5)(x + 1)*
Flamo:
;-;
Flamo:
@Hero you still here?
Flamo:
Never Mind, I took enough of your time anyway
Flamo:
(x - 5)(x + 1)
Flamo:
Check
Flamo:
Hm..
Flamo:
x(x - 1) + 5(x - 1)
Flamo:
x^2 - x + 5x - 5
Flamo:
-x subtract on 5x
Flamo:
x^2 -4x - 5
Flamo:
Oh.
Flamo:
@Shadow
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