Main content

### Course: Algebra 1 > Unit 14

Lesson 3: Solving by taking the square root- Solving quadratics by taking square roots
- Solving quadratics by taking square roots
- Quadratics by taking square roots (intro)
- Solving quadratics by taking square roots examples
- Quadratics by taking square roots
- Quadratics by taking square roots: strategy
- Quadratics by taking square roots: strategy
- Solving quadratics by taking square roots: with steps
- Quadratics by taking square roots: with steps
- Solving simple quadratics review

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Solving quadratics by taking square roots

Sal solves the equation 2x^2+3=75 by isolating x^2 and taking the square root of both sides. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- so plus or minus is basically like the math equivalent to

Schrödinger's cat?(39 votes)- You could say that. It's also like a quantum computer where it's binary can be a 0 or a 1 but it doesn't chose until you oberve it(16 votes)

- Why quadratic means 2, whether the word quad means 4? I'm confused about this, anyone can explain please?(8 votes)
- "Quad" is the start of a couple of different latin words - one that means four and a few others that relate to squares. In the case of quadratics, the quad- bit relates to the fact that the equations contain squares (and often relate to square shapes too).

Hope that helps - there's a more in-depth explanation here: http://mathforum.org/library/drmath/view/52572.html(15 votes)

- Where would you use Quadratics in real life? Like I know that algebra is really important, but are Quadratics specifically really going to be necessary when I'm not in school anymore?(6 votes)
- Well, lets just say you're going to be a carpenter/builder. If you need a triangle for a roof but you only have a square, you use the Pythagorean Theorem to find where to cut that square into a triangle to fit that roof.

https://www.khanacademy.org/math/in-seventh-grade-math/triangle-pror/right-angles-pythagoras/v/the-pythagorean-theorem(4 votes)

- Sal does the simple ones, but he doesn't show us how to do these: h(x)=−5x^2+180(3 votes)
- It is the same principle, set h(x)=0. This gives 0=-5x^2+180, then add 5x^2 to both sides to get 5x^2=180, divide by 5 to get x^2=36, so x = ±√36. This gives two solutions, x=-6 and x=6.(8 votes)

- Can't seem to have any idea about this one

(x-3)/8=2/(x-3)(3 votes)- You can also
*cross multiply*, which means you would get (x-3)(x-3)=16, the you would get x^2-6x+9=16, then x^2-6x-7, then (x-7)(x+1) so that the solutions would be +7 and -1(3 votes)

- Can somebody give me the definition of a Quadratic(1 vote)
- A quadratic is a 2nd degree polynomial, basically any polynomial that can be written in the form: Ax^2+Bx+C is a polynomial. A, B, and C are real numbers, and A can't = 0 (because if it did, you wouldn't have a 2nd degree polynomial).(7 votes)

- So, we have x^2 = 36

Could've we just take the principal square root of both sides, and then end up with |x| = 6 → x = ±6?(2 votes)- Yes absolutely.

That is actually what happens every time we take the square root of both sides.

Because mathematicians are lazy, we don't want to solve the absolute value equation, so we skip that step and jump straight to x = _+ 6, because that is what we will get.

In other words, what you did is 100% correct, but by jumping straight to x = _+ 6, you can skip a step.(4 votes)

- I am struggling to solve these problems I struggle with the 2nd step(2 votes)
- The first two steps are exactly like solving a two step linear equation. Two step equations require you to add/subtract first and then divide or multiply second. If you have x/2+5=13, you subtract 5 on both sides to get x/2=8, then opposite of divide is multiply by 2 to get x=16. Or if you have 3x - 2 = 10, add 2 to get 3x=12, divide by 3 to get x=4.

The only difference in the video is the third step of taking the square root, so x^2/2 + 5 = 13 gives x^2=16 giving x=+/- 4.(4 votes)

- how do you know when to use plus or minus for what X equals. Do you just choose either?(2 votes)
- When taking square roots the answer can either be a positive or negative number, so we use the plus or minus symbol to represent that.

Which value we use actually depends on the problem we are doing. If say, we are calculating a value for something like 'years since 2000' then that value can only be positive.

So if we are only dealing with positive values, we say we are taking the**principle square root**, which means we only use the positive value.

To be completely precise in math, we need to account for the different and include +/- before the number to make sure everyone looking at our value knows the actual value(s) we are dealing with.

Now, like I said if the value can't be negative then there is no reason to include the negative sign there.

Hope this helps!(3 votes)

- Is there a place I can do some practice problems for each lesson?(2 votes)
- Its really great because you can watch the video if your stuck or even get hints(2 votes)

## Video transcript

We're asked to
solve the equation 2x squared plus
3 is equal to 75. So in this situation,
it looks like we might be able to isolate
the x squared pretty simply. Because there's only one
term that involves an x here. It's only this x squared term. So let's try to do that. So let me just rewrite it. We have 2x squared
plus 3 is equal to 75. And we're going to try to
isolate this x squared over here. And the best way to do that,
or at least the first step, would be to subtract 3 from
both sides of this equation. So let's 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 want to isolate
this x squared. I have a 2x squared here. So I could have just
an x squared here if I divide this side or
really both sides by 2. Anything I do to one side, I
have to do to the other side if I want to maintain
the equality. So the left side, just
becomes x squared. And the right hand side
is 72 divided by 2 is 36. So we're left with x
squared is equal to 36. And then to solve for x,
we can take the positive, the plus or minus square
root of both sides. So we could say the plus or--
let me write it this way-- If we take the square
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
that 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
principal 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 could put them back
into the original equation to verify 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. Because negative 6
squared is also 36. 2 times 36 is 72 plus 3 is 75.