Question

a=4,b=−8,c=1
x1=1+1/2 √3
x2= 1-1/2 √3
Could anyone PLEASE walk me through this?

Answer 1

you want to use the quadratic formula to solve 4x^2 - 8x + 1 = 0 right?

Answer 2

Right

Answer 3

The quadratic formula is

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

Answer 4

Plug in the given values

a = 4
b = -8
c = 1

to get

\[\Large x = \frac{-(-8)\pm\sqrt{(-8)^2-4(4)(1)}}{2(4)}\]

Make sense so far?

Answer 5

I am following

Answer 6

ok now evaluate (-8)^2-4(4)(1) to get 48 and simplify -(-8) to get 8

so we get this next

\[\Large x = \frac{8\pm\sqrt{48}}{8}\]

Answer 7

from here, break up the plus/minus to get

\[\Large x = \frac{8+\sqrt{48}}{8} \ \text{or} \ x = \frac{8-\sqrt{48}}{8}\]

Answer 8

and simplify \[\Large \sqrt{48}\] to get \[\Large 4\sqrt{3}\]

so after that, the next step is

\[\Large x = \frac{8+4\sqrt{3}}{8} \ \text{or} \ x = \frac{8-4\sqrt{3}}{8}\]

do you see what to do from here?

Answer 9

divide by 8?

Answer 10

yes divide each part by 8 or break up the fractions and reduce


\[\Large x = \frac{8}{8}+\frac{4\sqrt{3}}{8} \ \text{or} \ x = \frac{8}{8}-\frac{4\sqrt{3}}{8}\]


\[\Large x = 1+\frac{1}{2}\sqrt{3} \ \text{or} \ x = 1-\frac{1}{2}\sqrt{3}\]

Answer 11

Thank you so much easier with step by step help

Answer 12

yw