How To Solve Quadratic Equations Using The Quadratic Formula

in this video we're going to talk about

how to solve quadratic equations using

the quadratic formula so let's start

with this one let's say we have the

equation 2x squared plus 3x minus 2 is

equal to 0 and our goal is to solve for

X we want to calculate the value of x

that makes this equation true so here is

the quadratic formula that we need to

use it's negative b plus or minus the

square root of b squared minus 4ac

divided by 2a now we need to know what a

B and C are equal to so in this format

where you have all of the X variables to

the left and 0 on the right a is the

number in front of X squared B is the

number in front of X and C is the

constant term so this is going to be I'm

going to rewrite it here X is equal to

negative B B is positive 3 plus or minus

the square root of B squared so that's 3

squared minus 4 times a a is 2 times C

which is negative 2 all divided by 2a or

2 times 2 so we have negative 3 plus or

minus the square root 3 squared is 9

negative 4 times 2 is negative 8 and

negative 8 times negative 2 is positive

16 on the bottom we have 2 times 2 which

is 4 now 9 plus 16 is 25 and the square

root of 25 is 5 so right now that's what

we have notice the plus or minus symbol

so we need to break this up into two

parts so we're gonna have negative 3

plus 5 divided by 4 and negative 3 minus

5 divided by 4 negative 3 plus 5 is

positive 2 negative 3 minus 5 is

negative 8 so right now we have two

different answers

now we can reduce to over four to one

over two if you divide both numbers by

two and 8 divided by 4 is negative 2 so

X can equal 1/2 or X can equal negative

2 and so that's how you can solve a

quadratic equation using the quadratic

formula now if you want to check your

answer you can plug it in let's plug in

negative 2 into this equation so we have

2 times the negative 2 squared plus 3

times minus 2 minus 2 let's see if that

equals 0 negative 2 squared is negative

2 times negative 2 which is 4 3 times

negative 2 is a negative 6 now 2 times 4

is 8 negative 6 minus 2 is negative 8 8

minus 8 is 0 so we know that this answer

works and you can try the other one too

that's going to work as well but now

let's move on to our next example let's

say we have this particular quadratic

equation go ahead and use the quadratic

formula to get the answer so we can see

that a is 6 B is negative 17 and C is 12

so let's begin by writing the formula so

it's x is equal to negative b plus or

minus the square root of b squared minus

4ac divided by 2a so b is negative 17

and then we have B squared that's

negative 17 squared minus 4a is 6 C is

12 divided by 2 a or 2 times 6 so we

have negative times negative 17 that

becomes positive 17 negative 17 squared

it's going to be positive 289 and then

we have negative 4 times 6 which is

negative 24 times 12 that's going to be

negative 288 2 times 6 is 12 and inside

the square root symbol we have 289 minus

288 which is the square root of 1 and

the square root of 1 is 1 so this is

what we now have so we have 17 plus 1

over 12 at this point when you have the

plus or minus symbol you can break it up

into two answers and the other answer is

going to be 17 minus 1 over 12 17 plus 1

is 18 and 17 minus 1 is 16 so now we

just need to reduce those fractions so

18 is 6 times 3 12 is 6 times 2

cancelling the 6 we get one of our

solutions as 3 over 2 for the other one

16 we can write that as 4 times 4 12 is

4 times 3 so cancelling the 4 we get the

other answer which is 4 over 3 and so

that's it for this video now you know

how to use the quadratic formula to

solve a quadratic equation thanks again

for watching