Question

PLSSS HELP!!! MEDALS!!!


Find all solutions to the following equation.

Answer 1

\[\sqrt{4x-3} +2=7\]

Answer 2

The first thing you need to do is get the square root all by itself on one side

That means you'll have to subtract 2 from both sides

Answer 3

okay and then what

Answer 4

subtract 2 from both sides
\[\Large \sqrt{4x-3} +2=7\]
\[\Large \sqrt{4x-3} +2{\color{blue}{-2}}=7{\color{blue}{-2}}\]
\[\Large \sqrt{4x-3} +0=5\]
\[\Large \sqrt{4x-3}=5\]

Answer 5

right

Answer 6

now you need to undo that square root. What operation is the opposite of square rooting?

Answer 7

squared

Answer 8

yes, square both sides and you'll get what equation?

Answer 9

4x-3=25

Answer 10

good

Answer 11

now solve for x like normal (that you've done previously with solving linear equations)

Answer 12

so x=7

Answer 13

can i ask you a question though

Answer 14

x = 7 is the possible answer
Make sure you plug this back into the original equation to check and confirm it

Answer 15

`can i ask you a question though` yes go ahead

Answer 16

why can't you just square the equation on both sides form the get go

Answer 17

You can. There's nothing stopping you. But it just makes everything more complicated than it has to be.

Answer 18

but when i did it that way I got x=12

Answer 19

so i'm not sure what i did wrong

Answer 20

hmm that's not correct. Show me your steps of what you did

Answer 21

alright its obviously wrong but
\[(\sqrt{4x-3}+2)^{2}=(7)^{2}\]
\[4x-3+4=49\]

Answer 22

you made an error when you squared the left side

Answer 23

it's tempting to think that (x+y)^2 = x^2+y^2, but that's not a true fact

Answer 24

instead it's really

(x+y)^2 = x^2 + 2xy + y^2

you have to use FOIL here

Answer 25

yeah i just realized that after typing it out thanks a bunch

Answer 26

no problem