Question

(5x+7)^2-14=0

Answer 1

Are we solving for x?

Answer 2

Yes

Answer 3

Have you considered adding 14?

Answer 4

Ok well let's start by multiplying (5x+7)(5x+7).
We will get:
(25x^2 +35x+35x+49)+14
Simplify.
25x^2+70x+63
Now we need to factor.

Answer 5

@tkhunny not until we factor

Answer 6

@nfcfox thank you for helping me get started on this

Answer 7

25x+35

Answer 8

Tbh tho tkhunny might be right about adding 14 as the factoring for including the +14 is making it harder.

Answer 9

thats the answer

Answer 10

Wait it's -14

Answer 11

Wait...can't it go farther than 25x+35 though?

Answer 12

5xtimes5x=25x 7times7=49 - 14 =25x+49-14=25x+35

Answer 13

Heavens! It already has the Square Completed. Let's just solve it.

Why bother to multiply it back out when it's already almost done. Since the answer will include \(\sqrt{14}\), there is no point in expanding and trying all over to factor something that you already know can't be factored.

(5x+7)^2-14=0

(5x+7)^2 = 14

\(5x+7 = \pm\sqrt{14}\)

\(5x = -7\pm\sqrt{14}\)

\(x = \dfrac{-7\pm\sqrt{14}}{5}\)

It's where the Quadratic Formula comes from. No harm in using it once in a while.

Answer 14

no it cant because that is a simple as it gets

Answer 15

@tkhunny thank you, I appreciate that

Answer 16

Let's go all the way back to 25x^2+70x+49-14
We will now get 25x^2+70x+35.
35 can factor into 1 and 35 which we can take the factors of 25 and 1 as well.

Answer 17

since theres a bunch of smart people of this has anyone read the short story called "the first seven years"?

Answer 18

Nevermind I screwed that up, i added wrong.

Answer 19

on this*

Answer 20

That can be factored like tkhunny showed earlier it's just gonna come out to some decimal.

Answer 21

This is why it is dangerous to get one idea in your head. If you decide which way to go - before looking at the problem - you can do an awful lot of stuff for no reason. Make your life simper. If there is a wonderfully easy process, use it. Unique answers don't care how you find them. Learn ALL methods. Learn ALL styles. Keep your mind open and your brain working.

Answer 22

seriously no one has read it

Answer 23

@tkhunny This is true! I get the formulas all mixed up and confused all the time and I need to be better about focusing on one method that would be the simplest way to go. Anyways, thank you for showing me how to work it out in the best way.

Answer 24

@CMILLIGAN123 no I have not read it

Answer 25

ok

Answer 26

BY EVERYONE!!i need to finish my homework

Answer 27

OKAY BYE NOW!