Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake.

f(x) = 2x^2 − 8x + 5
Line 1: f(x) = 2(x^2 − 8x) + 5
Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32
Line 3: f(x) = 2(x − 4)^2 − 27

Line 1
Line 2
Line 3
He did not make any mistakes
I think line 2, amirite?

Question

Marvin was completing the square, and his work is shown below. Identify the line where he made his mistake.

f(x) = 2x^2 − 8x + 5
Line 1: f(x) = 2(x^2 − 8x) + 5
Line 2: f(x) = 2(x^2 − 8x + 16) + 5 − 32
Line 3: f(x) = 2(x − 4)^2 − 27

Line 1
 Line 2
 Line 3
 He did not make any mistakes
I think line 2, amirite?

anonymous · Answer

yes, he didn't factor the 2 out correctly

dinamix · Answer

f(x) =2x^2-16x+5 this equation i think the answer is line 3

anonymous · Answer

oh wait, sorry. That factoring mistake is on line 1, not 2.

dinamix · Answer

yup this @peachpi  and he didnt right the correct must will f(x) = 2x^2-16x+5 and the aswer line 3

dinamix · Answer

2(x^2-4) @peachpi

anonymous · Answer

Y'all lost me

anonymous · Answer

$2x^2-8x$ = $2(x^2-4x)$ is what I meant

anonymous · Answer

they're asking you to find the mistake. The mistake is that the factoring on line 1 was wrong.

dinamix · Answer

all lines is wrong @peachpi

anonymous · Answer

yes, they're all wrong. But the mistake first happened on line 1

anonymous · Answer

Oh, alright, I see where you guys are coming from

dinamix · Answer

i think he made mistake in f(x) = 2x^2-8x+5 and should be 2x^2-16x+5  peachpi

dinamix · Answer

and the lines will be all correct

dinamix · Answer

did understand me @peachpi

anonymous · Answer

No. I don't know where you're getting that. The two expressions you typed aren't equal. This problem is about completing the square, which is basically rewriting the same thing in another way. You can't just change -8x to -16x because it changes the value of the expression.

dinamix · Answer

yup he did write it correct thats problem

dinamix · Answer

u didnt understand me  if the function f(x) = 2x^2-16x+5  we all lines  correct right ?

dinamix · Answer

find*

anonymous · Answer

No, because changing -8 to -16 changes the function. This is the correct solution to the problem, with no mistakes

$f(x)=2x^2-8x+5$

$f(x)=2(x^2-4x)+5$

$f(x)=2(x^2-4x+4)+5-8$

$f(x)=2(x-2)^2-3$

anonymous · Answer

Is he getting confused with the actual function? Hes really confusing me

anonymous · Answer

yeah I think so. If you compare what I have with the solution in the problem statement, you can see the mistake on the first line

anonymous · Answer

He didn't divide the 8x by the 2 you're factoring?

dinamix · Answer

@gigirained  are really this function f(x) = 2x^2-8x+5  are u sure its -8x not -16x ?

anonymous · Answer

yes correct @gigirained

anonymous · Answer

Positive its -8x

anonymous · Answer

@dinamix I see what you're doing. 
The objective of the problem is to find the mistake, if there is one. You're finding a function that matches the steps provided. So yeah if the initial function had -16x, then the work would be correct.

dinamix · Answer

ok he did mistake , didnt divide 8x by 2

dinamix · Answer

yup @peachpi  this why i check if write function correct or no

anonymous · Answer

Thanks you guys, @peachpi and @dinamix