Question

x ^2 - 12 = 5x + 2

Answer 1

you need to solve for x?

Answer 2

x^2-5x=14

Answer 3

x^2 = 5x + 14.

Answer 4

x^(2)-12=5x+2

Since 5x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 5x from both sides.
x^(2)-12-5x=2

Move all terms not containing x to the right-hand side of the equation.
x^(2)-5x-12=2

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
x^(2)-5x-14=0

In this problem 2*-7=-14 and 2-7=-5, so insert 2 as the right hand term of one factor and -7 as the right-hand term of the other factor.
(x+2)(x-7)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+2=0_x-7=0

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2_x-7=0

Set each of the factors of the left-hand side of the equation equal to 0.
x=-2_x-7=0

Since -7 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 7 to both sides.
x=-2_x=7

The complete solution is the set of the individual solutions.
x=-2,7

Answer 5

the underscores are just spaces

Answer 6

@thewonderfuladele That's really elaborate.

Answer 7

x^2 + -12 = 5x + 2 ----> -12 + x^2 = 5x + 2 ----> -12 + x^2 = 2 + 5x.
-12 + -2 + -5x + x^2 = 2 + 5x + -2 + -5x -----> -12 + -2 = -14
-14 + -5x + x^2 = 2 + 5x + -2 + -5x -----> -14 + -5x + x^2 = 2 + -2 + 5x + -5x.

2 + -2 = 0 ----> -14 + -5x + x^2 = 0 + 5x + -5x ----> -14 + -5x + x^2 = 5x + -5x. 5x + -5x = 0 ----> -14 + -5x + x^2 = 0. (-2 + -1x)(7 + -1x) = 0 <----

-2 + -1x = 0
-2 + -1x = 0
-2 + 2 + -1x = 0 + 2
2 + 2 = 0
0 + -1x = 0 + 2 ----> -1x = 0 + 2
0 + 2 = 2 ----> -1x = 2

x = -2

Answer 8

Then -

7 + -1x = 0
7 + -7 + -1x = 0 + -7 ----> 7 + -7 = 0 ----> 0 + -1x = 0 + -7 -----> -1x = 0 + -7.

0 + -7 = -7 ----> -1x = -7.

x = 7

Answer 9

Thus -
x = -2. x = 7.

Answer 10

WAIT WAIT WAIT GUYS LOOK

Answer 11

WHAT

Answer 12

hmm?

Answer 13

x^2-5x-14
ok?

Answer 14

factor it

so

(x-7)(x+2)

x=7; -2

Answer 15

Oh wow
LOL

Answer 16

Yeah haha it just clicked.

SO yeah thats SOOOOOOOOOOO much easier, right?
and it makes sense?

Answer 17

YES

Answer 18

Clean - Easy - Wow

Answer 19

whydidinotseethatbefore.

the only question left isss does @JoStudy get it? get how I factores it

Answer 20

Yeah, it's easy. It's just best to elaborate so people see the inner works.
Good job.

Answer 21

Thanks everybody! And can you explain thaht @klakelyn ?

Answer 22

No problem!

Answer 23

sure hang on @JoStudy

Answer 24

since you have
x^2-5x-14
you need to factor it
to factor it you need to find 2 values that multiply together to get -14, and when they are added you get -5.

Answer 25

so the factors of -14 are
1,-14 or -1,14
or 2,-7 or -2,7

Answer 26

-7 and 2 multiply out to get -14 and add together to get -5.

when you get your factor as
(x-7)(x+2) you multiply it out to check your work

use F(irst)O(uter)I(nner)L(ast)
FOIL
so

Answer 27

@JoStudy

x^2+2x-7x-14
x^2-5x-14


does that make sense?

Answer 28

Thanks!

Answer 29

No probs:)