Question

@jim_thompson5910 Do you mind helping me with quadratic Formulas?

Answer 1

Like, I wanna know how to do them.

Answer 2

For a quadratic equation \[ax^2+bx+c=0\]\[x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]

Answer 3

Just plug your a, b, and c into the equation to find x.

Answer 4

Ok..like..Can you give me an example?

Answer 5

say you want to solve

2x^2 - 3x - 20 = 0

for x

Answer 6

compare 2x^2 - 3x - 20 to ax^2 + bx + c

we see that

a = 2
b = -3
c = -20

Answer 7

plug these values into the quadratic formula

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

\[\large x=\frac{-(-3) \pm \sqrt{(-3)^2-4(2)(-20)}}{2(2)}\]

\[\large x=\frac{3 \pm \sqrt{169}}{4}\]

\[\large x=\frac{3 \pm 13}{4}\]

\[\large x=\frac{3 + 13}{4} \ \text{ or } \ x = \frac{3 - 13}{4}\]

\[\large x=\frac{16}{4} \ \text{ or } \ x = \frac{-10}{4}\]

\[\large x=4 \ \text{ or } \ x = -\frac{5}{2}\]


--------------------------------------------------------------------


So the two solutions to 2x^2 - 3x - 20 = 0 are x = 4 or x = -5/2

Answer 8

Ok. I *think I got it. What If i had the problem y^2-81=0.

Answer 9

What would I do then?

Answer 10

if you want to use the quadratic formula, then think of y^2-81 as y^2+0y-81

Answer 11

so

a = 1
b = 0
c = -81

Answer 12

Oh...Ok...I need help on this though..
x^2 - 3x - 10 = 0...Im going to try it and see what I get. Can you tell me if I got it right or wrong?

Answer 13

sure, post what you get

Answer 14

My:
a:1
b:-3
c:-10. Right?

Answer 15

correct

Answer 16

plug those values into the quadratic formula

Answer 17

I got:
\[x=\frac{ 3\pm \sqrt{-50} }{ 2 }\]
Is that right?

Answer 18

b^2 - 4ac = (-3)^2 - 4(1)(-10)

b^2 - 4ac = 9 + 40

b^2 - 4ac = 49

Answer 19

not sure how you got -50

Answer 20

I got it by multiplying the - times a positive..Like i did it in order. Multiplied the 3 subtracted that from 4 then multiplied it by 1 then multiplied it by -10. I dunno..Lemme check

Answer 21

do you see how I got 49?

Answer 22

Ooooo...Ok. I got it. I did it the wrong way....I see what you did. What would I do after that step?

Answer 23

you break up the plus/minus to get these two equations

x = (3 + 49)/2 or x = (3 - 49)/2

Answer 24

oops sry

Answer 25

I think it'd be:
\[x= \frac{ 3\pm \sqrt{7} }{ 2 }\]

Answer 26

the square root of 49 is 7, so these two equations

x = (3 + 7)/2 or x = (3 - 7)/2

Answer 27

once you take the square root of a number, the square root symbol goes away

Answer 28

oh. Ok. So that way it'll be just + or -. Got it!!!!:) Thank You!!!!

Answer 29

you're welcome