Question

What is the solution to the equation? HELLLP!!!

Answer 1

\[\sqrt{2X+13} - 5 = X\]

Answer 2

@jim_thompson5910

Answer 3

HI!!

Answer 4

1) add \(5\)

Answer 5

Hi! Can you please help?

Answer 6

2) square

Answer 7

to both sides?

Answer 8

go ahead and do those, i will check
yes of course
what you do to one side, you do to the other

Answer 9

\[\sqrt{2x+13}-5=x\]\[\sqrt{2x+13}=5x\]

Answer 10

right?

Answer 11

oh no dear, don't multiply \(5x\) means \(5\times x\)
you want to ADD

Answer 12

\[\sqrt{2x+13}=x+5\]

Answer 13

? like that?

Answer 14

yes

Answer 15

now what? I dont understand what you mean by square? And thanks

Answer 16

much better
now square both sides so you get rid of the radical on the left

Answer 17

square means to multiply it by itself
you need to get rid of the square root, so you do that by squaring it

Answer 18

So\[2x ^{2}+13^{2}=x^{2}+5^{2}\]
\[4x+169=x^{2}+25\]

Answer 19

?

Answer 20

or would the 4x be \[4x^{2}\]

Answer 21

ok lets go back up slowly q

Answer 22

we got \[\sqrt{2x+13}=x+5\]
when you square the left, you just get \(2x+13\)

Answer 23

in other words, the radical goes bye bye
that is the whole point

Answer 24

so we get
\[2x+13=(x+5)^2\] as the next step

Answer 25

Oh okay! I see. then \[x ^{2}+25\]

Answer 26

or no?

Answer 27

oooh no don't make that mistake or your teacher will think you are a moron
you don't want that !

Answer 28

lol.. okay.. then what do i do?

Answer 29

\[(x+5)^2=(x+5)(x+5)=x^2+5x+5x+25=x^2+10x+25\]

Answer 30

wait what?

Answer 31

square means multiply by itself

Answer 32

some teachers like to call that "foil" maybe you heard it that way

Answer 33

yeah, and x * x is x^2? and 5*5 is 25? i thought...

Answer 34

yea i know what you thought
you thought you could square each piece separately

Answer 35

and yes, there is an \(x^2\) in the answer, as well as a \(25\) but it is not
\[(x+5)^2=x^2+25\] like i said DO NOT MAKE THAT MISTAKE
it is \((x+5)^2=x^2+10x+25\)

Answer 36

okay. now what?

Answer 37

ok now it has been so long we start at the top and go quicker
\[\sqrt{2x+13} - 5 = x\] add 5\[\sqrt{2x+13}=x+5\] square (correctly)\[2x+13=x^2+10x+25\] now you have a quadratic equation to solve

Answer 38

subtract \(2x\) and \(13\) to set it equal to zero, get
\[x^2+8x+12=0\] and now solve for \(x\) by factoring if you can

Answer 39

\[8x^{2}=-12?\]

Answer 40

or no?

Answer 41

no

Answer 42

or \[x^{2} + 8x=-12\]

Answer 43

oh no?

Answer 44

do you know how to factor?

Answer 45

No. :/

Answer 46

hmm that is a problem
because you really want to turn \[x^2+8x+12=0\] in to
\[(x+2)(x+6)=0\]

Answer 47

How did you get 2 and 6?

Answer 48

have you spent any time solving quadratic equations ?

Answer 49

i got them because \(2\times 6=12\) and \(2+6=8\)

Answer 50

No, I missed 3 years of highschool because I had lynch syndrome(cancer), I was NEVER there to learn anything. I am pretty much teaching myself through the course of online schooling just trying to pass and get to college. and I see. So you find two numbers that can go into both of them?

Answer 51

two numbers whose product is 12 and whose sum is 8 yes

Answer 52

okay, i understand. so then do we do that foil thing you talked about?

Answer 53

now that we have \[(x+2)(x+6)=0\] we solve
\[x+2=0\] and get \(x=-2\) and also \(x+6=0\) to get \(x=-6\)

Answer 54

then we go back to the original equation and try them out

Answer 55

okay, I see. so we plug it in?

Answer 56

\[\sqrt{2(-2)+13}-5=-6\]

Answer 57

?

Answer 58

yes \[\sqrt{2x+13}-5=x\]
\[\sqrt{2\times (-2)+13}-5=-2\] true for faclse

Answer 59

false? Shouldnt it be =-6?

Answer 60

the right sides should be \(-2\) because it is x

Answer 61

we will try \(-6\) second

Answer 62

okay

Answer 63

now we are trying \(x=-2\) which means everywhere

Answer 64

okay I see. so \[\sqrt{2(-2)+13}-5=-2\]

Answer 65

\[\sqrt{2\times (-2)+13}-5=-2\] works because you get
\[\sqrt{-4+13}-5=\sqrt{9}-5=3-5=-2\checkmark\]

Answer 66

Okay, so is that all we do?

Answer 67

no, now we try \(x=-6\) to see if that works

Answer 68

\[\sqrt{2(-6)+13}-5=-6?\]

Answer 69

\[\sqrt{-12+13} -5=-6\]

Answer 70

this one does not work
we get
\[\sqrt{1}-5=1-5=-4\neq -6\]

Answer 71

so it would be -2?

Answer 72

whew yes, after all that

Answer 73

so lets see what we needed to do this
a) a method
b) knowing how to square correctly
c) solving a quadratic equation
d) knowing to check the answer

Answer 74

So that is the final answer?

Answer 75

yes final answer is -2

Answer 76

Thank you soooo much.

Answer 77

i would suggest that the other stuff is somewhat more important than this
but no matter you do what you have to
your welcome \(\color\magenta\heartsuit\)