Use the quadratic formula to

solve the equation, negative x squared plus 8x is equal to 1. Now, in order to really use the

quadratic equation, or to figure out what our a’s, b’s and

c’s are, we have to have our equation in the form, ax

squared plus bx plus c is equal to 0. And then, if we know our a’s,

b’s, and c’s, we will say that the solutions to this equation

are x is equal to negative b plus or minus the square root

of b squared minus 4ac– all of that over 2a. So the first thing we have to

do for this equation right here is to put it

in this form. And on one side of this

equation, we have a negative x squared plus 8x, so that looks

like the first two terms. But our constant is on

the other side. So let’s get the constant on the

left hand side and get a 0 here on the right hand side. So let’s subtract 1 from both

sides of this equation. The left hand side of the

equation will become negative x squared plus 8x minus 1. And then the right hand

side, 1 minus 1 is 0. Now we have it in that form. We have ax squared

a is negative 1. So let me write this down.

a is equal to negative 1. a is equal to negative 1. It’s implicit there, you could

put a 1 here if you like. A negative 1. Negative x squared is the same

thing as negative 1x squared. b is equal to 8. So b is equal to 8, that’s

the 8 right there. And c is equal to negative 1. That’s the negative

1 right there. So now we can just apply

the quadratic formula. The solutions to this equation

are x is equal to negative b. Plus or minus the square root

of b squared, of 8 squared, minus 4ac– let me do it in that

green color –minus 4, the green is the part

of the formula. The colored parts are the things

that we’re substituting into the formula. Minus 4 times a, which is

negative 1, times negative 1, times c, which is

also negative 1. And then all of that– let me

extend the square root sign a little bit further –all

of that is going to be over 2 times a. In this case a is negative 1. So let’s simplify this. So this becomes negative 8, this

is negative 8, plus or minus the square root

of 8 squared is 64. And then you have a negative 1

times a negative 1, these just cancel out just to be a 1. So it’s 64 minus is 4. That’s just that 4 over there. All of that over negative 2. So this is equal to negative

8 plus or minus the square root of 60. All of that over negative 2. And let’s see if we can

simplify the radical expression here, the

square root of 60. Let’s see, 60 is equal

to 2 times 30. 30 is equal to 2 times 15. And then 15 is 3 times 5. So we do have a perfect

square here. We do have a 2 times

2 in there. It is 2 times 2 times

15, or 4 times 15. So we could write, the square

root of 60 is equal to the square root of 4 times the

square root of 15, right? The square root of 4 times

the square root of 15, that’s what 60 is. 4 times 15. And so this is equal to– square

root of 4 is 2 times the square of 15. So we can rewrite this

expression, right here, as being equal to negative 8 plus

or minus 2 times the square root of 15, all of that

over negative 2. Now both of these terms right

here are divisible by either 2 or negative 2. So let’s divide it. So we have negative 8 divided

by negative 2, which is positive 4. So let me write it over here. Negative 8 divided by negative

2 is positive 4. And then you have this

weird thing. Plus or minus 2 divided

by negative 2. And really what we have

here is 2 expressions. But if we’re plus 2 and we

divide by negative 2, it will be negative 1. And if we take negative 2 and

divide by negative 2, we’re going to have positive 1. So instead of plus or minus, you

could imagine it is going to be minus or plus. But it’s really the same thing. Right? It’s really now minus or plus. If it was plus, it’s now

going to be a minus. If it was a minus, it’s now

going to be a plus. Minus or plus 2 times the

square root of 15. Or another way to view it is

that the two solutions here are 4 minus two roots of 15,

and 4 plus two roots of 15. These are both values of x

that’ll satisfy this equation. And if this confuses you, what I

did, turning a plus or minus into minus plus. Let me just take a little

bit of an aside there. I could write this expression

up here as two expressions. That’s what the plus

or minus really is. There’s a negative 8 plus 2

roots of 15 over negative 2. And then there’s a negative

8 minus 2 roots of 15 over negative 2. This one simplifies to–

negative 8 divided by negative 2 is 4. 2 divided by negative

2 is negative 1. 2 times a 4 minus the

square root of 15. And then over here you have

negative 8 divided by negative 2, which is 4. And then negative 2 divided by

negative 2, which is plus the square of 15. And I just realized I made

a mistake up here. When we’re dividing a 2 divided

by negative 2, we don’t have this 2 over here. This is just a plus or

minus the root of 15. We just saw that when

I did it out here. So this is minus the

square root of 15. And this is plus the

square root of 15. So the two solutions for this

equation– It’s good that I took that little hiatus there,

that little aside there. The two solutions could be 4

minus the square root of 15, or x, or and, x could be 4 plus

the square root of 15. Either of those values of x

will satisfy this original quadratic equation.

thanks for explaining !

You make this look like shooting fish in the barrel xD

thanks

I thought the formula for when "b" is an even number, it's "x= -b' squared plus or minus the square root of b' squared minus ac over a"?? so wouldn't the formula be "ax squared + 2b'x +c= 0 when a doesn't equal 0"

wouldn't that be the quadratic formula II? 8 is an even number, so i thought you use the quad. formula 2 for when the coefficient of x is an even number, and use the quadratic formula 1 when the coefficient of x is an odd number.

so easy

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so easy

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so easy

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Breaking down the square was very helpfull info. Thanks again!

could someone please explain why let's say

-8 + 2 all over -2 is 4-1 and not 4 + 2… wouldn't the -2 as the denominator cancel out with the -8 and become 4? why is it not so?

This man is a genius! ðŸ˜€

it really helped me with my homework i subscribed.

there must be some mistake . i think the answers are 4-rad(15) and 4+rad(15)

5:12 you forgot to divide by two. its 4-âˆš15 or 4+âˆš15.

Hope you understand.