Question

solve using quadratic formula with steps x^2-x-30=0

Answer 1

I can solve it without the quadratic formula

Answer 2

oh how

Answer 3

Well, there's three ways you can solve it without the quad formula:

1. Graph It
2. Complete The Square
3. Factor By Grouping

Answer 4

no thanks i need to learn quadratic formula

Answer 5

Graphing is the easiest of course, but it requires a graphing calc

Answer 6

Well, when using the quadratic formula, you always have to identify a, b, and c. Do you know how to do that?

Answer 7

yes

Answer 8

a=x^2 b=-x c= -30

Answer 9

Good, that will help you

Answer 10

Now, the only thing we have to do is know the quadratic formula and input the values of a, b, and c into it, then simplify

Answer 11

ok i usually have trouble simplfing it because idk wht step is first

Answer 12

\[\frac{-b \pm \sqrt{b^2-4ac}}{2a} \]

Answer 13

I see, well, we will plug in the values of a,b, and c first. You always use order of operations when simplifying expressions. The square root is the same as an exponent, so you have to evaluate that first.

Answer 14

in the square root should be x^2-4(x^2)(-30)

Answer 15

Oh wait....your a, b, and c are incorrect

Answer 16

a, b, and c, are numbers only that come before the variables in each term

Answer 17

oh?

Answer 18

x^2-x-30=0
a=1 b= -1 c = -30

Answer 19

excellent

Answer 20

Now what goes inside the square root?

Answer 21

-1^2-4(1)(-30)

Answer 22

(-1)^2 -4(1)(-30)

Good but make sure you put the -1 inside parentheses

Answer 23

Because you will be squaring -1

Answer 24

which would make it 1

Answer 25

Yes

Answer 26

1-4(1)(-30)

Answer 27

excellent

Answer 28

now what

Answer 29

Now you finish simplifying everything inside the square root

Answer 30

how?

Answer 31

Order of operations still apply

Answer 32

You multiply first before subtracting

Answer 33

multiply (1)(-30)?

Answer 34

Multiply 4*1*-30

Answer 35

-120?

Answer 36

yes, now you have 1-(-120)

Answer 37

121

Answer 38

very good. Do you know how to take the square root of that?

Answer 39

well i normally wld use a calculater but i dont have one

Answer 40

What is 11*11?

Answer 41

121

Answer 42

Yes, so the square root of 121 is 11

Answer 43

ok so now its 1+-11/?

Answer 44

\[\frac{1 \pm 11}{2*1}\]

Answer 45

1±11/2

Answer 46

well, actually if you put it in that form, it isn't correct

Answer 47

oh?

Answer 48

\[(1\pm 11)/2\]

Answer 49

You have to make sure you put parentheses, that way we know that the whole numerator is divided by 2, not just 11/2

Answer 50

ok

Answer 51

It's what happens when you use the linear form

Answer 52

how do i diivode tht by two

Answer 53

If you write it as a top down fraction, you can leave it as:

\[x = \frac{1 \pm 11}{2}\]

Answer 54

Usually, you just leave it in that form because dividing by two would give decimals instead of whole numbers. We started with whole numbers so we should leave the answer in whole numbers

Answer 55

if i am aloud to use deciamls what do i do

Answer 56

i canuse deciamls rounded to the nearest tenth

Answer 57

Then you can write it as:

\[x = .5 \pm 5.5 \]

Answer 58

there positive?

Answer 59

Or you can split it up into two values of x:

x = -5
x = 6

Answer 60

So in fact, we do end up with whole numbers, so you can put that as the answer

Answer 61

thank you so much i really appreciate it :)