Simple Quadratic Equation

u16_l5_t1_we1 Simple Quadratic Equation

We're asked to solve the equation 2x squared plus 3 = 75.

So in this situation looks like we might be able to isolate the x squared pretty simply. 'Cause

there's only one term that involves an x here. It's the only

x squared term. So lets try to do that. So let me just rewrite

it.

So 2x squared + 3 = 75. I'm going to try to isolate this x squared

over here. The best way to do that

or at least the first step, would

be the subtract 3 from both sides of this equation.

So lets subtract 3 from both sides.

The left hand side we're just left with 2x squared. That was the whole point of subtracting 3 from both sides.

And on the right hand side 75 minus 3 is 72.

Now I wanna isolate this x squared, I have a 2x squared here.

So I could have just have an x squared here if I divide

this side

or

really both sides by 2. Anything that I do on 1 side,

I have to do the other side.

If I want them to mantain the quality.

So the left side just becomes x squared.

And the right hand side, the 72 divided by 2 is 36. So we're up with x

squared

is

equal

to

36.

And then to solve for x we can take the positive plus or minus

squared root of both sides. So we can say the plus or

let me right it this way.

If we take the squared root of both sides, we would get x

is

equal

to

the plus or minus square root of 36. Which is equal to plus or minus

6. let me just write it on another line.

So x is equal to plus or minus 6.

And remember here!

If something squared is equal to 36, that something could be the negative

version, or the positive version.

It could be the principle root, or it could be the negative root.

Both negative 6 squared is 36 and positive 6 squared is 36.

So both of these work. And you can put them back into the original

equation, to varify it. Let's do that. If you say

2 times 6 squared plus 3, that's 2 times 36 which is 72

plus 3 is 75. So that works.

If you put negative 6 in there, you're going to get the exact same result.

Cause negative 6 squared is also 36, 2 times 36 is 72,

plus 3 is 75.