Question

solve the equation: √x+6+√2-x=4

Answer 1

\[\sqrt{x+6}+\sqrt{2-x}=4?\]

Answer 2

yeah, that's my question

Answer 3

\[\sqrt{x+6}=4-\sqrt{2-x}\]

Answer 4

i don't know how to type it just like that in the posts..

Answer 5

first thing i did was subracted sqrt(2-x) on both sides

Answer 6

now i'm going to square both sides

Answer 7

remember
\[(a+b)^2=a^2+2ab+b^2\]
\[(\sqrt{x+6})^2=(4-\sqrt{2-x})^2\]
\[x+6=15-2(4)(\sqrt{2-x})+(\sqrt{2-x})^2\]

Answer 8

oops 4^2 is 16

Answer 9

type-o

Answer 10

\[x+6=16-2(4)\sqrt{2-x}+(\sqrt{2-x})^2\]

Answer 11

\[x+6=16-8\sqrt{2-x}+(2-x)\]

Answer 12

now we simplify and put sqrt{2-x} by itself on one side
\[x+6=18-x-8\sqrt{2-x}\]
\[x+x+6-18=-8\sqrt{2-x}\]

Answer 13

\[2x-12=-8\sqrt{2-x}\]
we can leave the -8 there in front of the sqrt{2-x}
now square both sides
\[(2x-12)^2=(-8\sqrt{2-x})^2\]

Answer 14

lol

Answer 15

\[4x^2-2(2)(12)x+144=64(2-x)\]
\[4x^2-48x+144=128-64x\]
see we don't have any square root thingy ma jiggers to worry about now

Answer 16

now we put everything on one side
and see if we can factor
or we can use the quadratic formula

Answer 17

\[4x^2-48x+64x+144-128=0\]

Answer 18

\[4x^2+16x+ 16=0\]

Answer 19

now each term has the factor 4 in common
we can factor 4 out
and then divide both sides by 4
\[x^2+4x+4=0\]

Answer 20

this can easily be factored
(x+2)^2=0

Answer 21

x+2=0
x=-2

Answer 22

that seemed like a lot of work and you just whipped it out like nothing. THANK you, first person where they actually care about helping and explaining

Answer 23

i don't see the point in just giving an answer without an explanation

Answer 24

i very much appreciate that!! you have NO idea

Answer 25

np