Question

Solve x2 + 8x − 3 = 0 using the completing-the-square method. (2 points)



x = four plus or minus the square root of three
x = negative four plus or minus the square root of three
x = four plus or minus the square root of nineteen
x = negative four plus or minus the square root of nineteen

Answer 1

do you know what value of k we can choose so the following is true:
\[x^2+8x+?^2=(x+?)^2\]

Answer 2

value of ?*

Answer 3

hint: recall the following:
\[x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2\]

Answer 4

ok

Answer 5

im still confused

Answer 6

examples:
\[x^2+2x+1=(x+1)^2 \\ x^2+4x+4=(x+2)^2 \\ x^2+6x+9=(x+3)^2 \\ x^2+8x+?^2=(x+?)^2\]

Answer 7

notice the 3rd term on the left hand side is just the number in front of x divided by two then squared
this is why we have:
\[x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2\]

Answer 8

but which one is it then??

Answer 9

@imqwerty
can u help me?

Answer 10

8 divided by 2 is 4...

Answer 11

\[x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2 \\ x^2+8x+(\frac{8}{2})^2=(x+\frac{8}{2})^2 \\ \]


so you have after simplifying:
\[x^2+8x+4^2=(x+4)^2 \\ \text{ or } \\ x^2+8x+16=(x+4)^2 \]

Answer 12

\[x^2+8x-3=0 \\ x^2+8x=3 \\ x^2+8x+\text{ ___ }=3+ \text{___}\]

Answer 13

so what do you need to add on both sides to complete the square on the left hand side

Answer 14

sqr root

Answer 15

\[x^2+8x+16 \text{ is } (x+4)^2 \\ x^2+8x+ \text{___}=3+\text{___}\]
so you need to add 16 on both sides in order to complete the square on the left hand side

Answer 16

did you want to tell me how far you gotten?

Answer 17

I could check your work so far.

Answer 18

well if get back my notifications aren't working
so try mentioning me