Question

Solve by completing the square
x^2-20x+30=0

Answer 1

using this would help you and remember the a=1, b=-20, and c=30

Answer 2

\[x^2-2*x*10+10^2-10^2+30=0\]

Answer 3

what do you do after that? @surjithayer

Answer 4

do i used the quadratic formula to solve by completing squares? @KaiserTheSlayer

Answer 5

yes

Answer 6

so it would be x=18.36660026534076
and x= 1.63339973465925

Answer 7

oh okay thank you

Answer 8

yup

Answer 9

Solving by square completion yields:\[x²-20x=-30\]\[x²-20x + 100 = 70\]\[(x-10)²=70\] There you have it. Do you the step-by-step?

Answer 10

no i don't

Answer 11

\[(x-10)^2-100+30=0\]
\[\left( x-10 \right)^2=70=\left( \sqrt{70} \right)^2\]
\[x-10=\pm \sqrt{70}\]
x=?

Answer 12

where is the 100 coming from?

Answer 13

You take half of the x coefficient, square it and add to both sides.

Answer 14

thats right! i sorta remember now

Answer 15

Don't forget to divide everything by whatever is multiplying the squared term ;). In this case, it's "1", so it won't matter.

Answer 16

so then to figure out what x is I solve... x-10=\[\sqrt{70}\]
and x-10=\[\sqrt{-70}\]

Answer 17

idk why it looks like that i was trying to write what you did on the last thing

Answer 18

Be careful! The second solution you gave is a COMPLEX number.

Answer 19

i know i have to do the whole i stuff for that cause its a negative square root

Answer 20

No, it's not:\[x-10=\sqrt{70} \]or\[x-10=-\sqrt{70}\]

Answer 21

notice the minus sign is outside.

Answer 22

yeah i see that now

Answer 23

And that's it! you have your solutions! Just move the independent term to the other side.

Answer 24

yeah i got it now, thank you!

Answer 25

The whole thing about completing the square is to make the left side equation look like something like (x-a)² or (x+a)²