Question

please help..... expalin in steps

4x2 - 32x + 16 = 0

answers;

(x - 4)2 = 12 (x + 4)2 = -12
(x - 16)2 = 1 (x + 16)2 = -1

Answer 1

Okay, we need to solve for x.

Answer 2

okay i got you

Answer 3

This is a quadratic equation, so we use the quadratic formula.

Answer 4

I'll put it up here.

Answer 5

\[x = \frac{ -b \sqrt{b^{2}-4ac} }{ 2a }\]

Answer 6

4x^2 - 32x + 16 = 0

b = 32
a = 4
c = 16

Answer 7

So now we plug those values into the formula.

Answer 8

\[x = \frac{ -32 \sqrt{b^{2}-4(4)(16)} }{ 2(4) }\]

Answer 9

Oops, left out b for b^2 one second :D

Answer 10

\[x = \frac{ -32 \sqrt{32^{2}-4(4)(16)} }{ 2(4) }\]

Answer 11

So now we solve what's under the sqrt like so:
\[\sqrt{32^{2} - 256 }\]
\[\sqrt{1024 - 256}\]
\[\sqrt{768}\]

Answer 12

So now we have:
\[x = \frac{ -32\sqrt{768} }{ 8 }\]

Answer 13

thanx this was a long problem so thanx for sticking around :))

Answer 14

No problem, almost done.

Answer 15

kay ^^

Answer 16

So now:
\[x = \frac{ -512\sqrt{3} }{ }\]

Answer 17

over 8

Answer 18

x = -64 over sqrt 3

Answer 19

notice in
\[ 4x^2 - 32x + 16 = 0 \]
that each term can be evenly divided by 4.
so let's divide both sides of the equation by 4 (that means each term, on both sides)
\[ \frac{4}{4} x^2 - \frac{32}{4} x + \frac{16}{4}= \frac{0}{4} \]
which simplifies to
\[ x^2 -8x +4 = 0\]
based on the answer choices, it looks like we should COMPLETE THE SQUARE
do you know how to do that ?

Answer 20

I didn't even see the answer choices. *facepalm*

Answer 21

to complete the square, start by "moving" the 4 to the right side of the equation. You do this by add -4 to both sides:
\[ x^2 -8x +4 - 4 = 0 - 4 \\ x^2 -8x = -4 \]

Answer 22

the next step is look at the number in front of the x. The coefficient is -8

divide the coefficient by 2, and then square the result: -8/2 = -4
square -4: -4* -4 = +16

add +16 to both sides:
\[ x^2 -8x +16= -4 +16\]

the left side is a perfect square. the right side simplifies