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### Course: Digital SAT Math > Unit 8

Lesson 7: Solving quadratic equations: medium# Solving quadratic equations — Basic example

Watch Sal work through a basic Solving quadratic equations problem.

## Want to join the conversation?

- Wait, when Sal does the 4x^2= 52 example, he says that the solution is +√13 and -√13. If we plug in the -√13 into the original quadratic equation, doesn't the negative sign remain because it is outside the square root sign? So, isn't -√13 not a solution to the quadratic equation?(8 votes)
- When you plug in a value for x, it behaves as if it were contained within parentheses for the purpose of order of operations. So 4x^2=52 becomes 4(-√13)^2 = 52, which in turn means 4 (-√13)(-√13) = 52. Since you square the entire -√13 expression, the negative cancels itself out, leaving you with 13.

What you are thinking about is something like -3^2, which is in fact -9, because order of operations suggests it is actually (-1)(3)^2 = (-1)(3)(3) = (-1)(9) = -9. If you were plugging -3 into an equation to replace x, such as x^2, then it would be evaluated as (-3)^2, or simply, 9.(30 votes)

- Why positive or negative in the square root?(4 votes)
- Well, if we start with
`x² = 9`

we know that something times itself is 9

We know immediately that x can equal 3, because`3 x 3 = 9`

However, we have to put on the brakes here, because there is another way to get 9 by multiplying negative 3 by itself:`-3 x -3 = 9`

Because of that, if we are solving x² = 9, we have to allow for either correct answer.

So we say, x = ± 3 and that means that x = 3 or x = -3

When we have the more complicated case of`x² = 13`

the square root will be x = ± √13 and that means we have two possible answers:

x = +√13 and x = - √13

You have to be careful, though, because if the problem says

What is √16 , this only has one answer. √16 means`give me the principal square root of 16`

and that is asking for only the**positive**root.(38 votes)

- Please Sal, am finding it hard to solve the word problem questions, even after watching videos examples which i find explanatory, i just keep getting wrong answers during practice. please help me.(10 votes)
- Why cant i just wake up with a 1500+ score(6 votes)
- Because happiness has to be fought for.(8 votes)

- I thought you can't have a negative under the radical. I don't see how you can say "the square root of negative 13?"(4 votes)
- It's not "the square root of negative 13", it's "the negative square root of 13".

For example, if you have 4, its positive square root is 2, its negative square root is -2.(9 votes)

- When you say the sqrt of 13 aren't you allowing for both the negative and positive already?(8 votes)
- Wait, when Sal does the 4x^2= 52 example, he says that the solution is +√13 and -√13. If we plug in the -√13 into the original quadratic equation, doesn't the negative sign remain because it is outside the square root sign? So, isn't -√13 not a solution to the quadratic equation?(5 votes)
- It is a solution because ( -√13 )^2 is 13 and 13*4 =52.(4 votes)

- does equations that have x^2 always have 2 answers, what about ones with just x(4 votes)
- You right! The equation x^2 would have two answers, because when you have something that is square rooted it has a positive and a negative root. X would only have one answer because it would be what ever X was. Try going to a online graphing calculator called Desmos and plug those in and you will see that it crosses the x axis twice for the first one and once or the second one.(3 votes)

- What is the difference between √13 and 13? I get that's it's a square root symbol but it doesn't make sense to me. Couldn't the answer also be -13 and 13 to this equation?(3 votes)
- Not at all. √13 is roughly equal to 3.606 because when you square 3.606, you get 13. Squaring and taking the square root are inverse equations, squaring multiplies the number by itself, taking the square root gives you the number you would need to square to get that original number.

Make sense?(4 votes)

- Why is there positive or negative in square root? why is it important to the equation?(3 votes)
- When you take the square root of something, you're asking yourself: "What number would I have to multiply by itself to get this number that I'm taking the square root of". If you multiply any number by itself, regardless of whether its positive or negative, the answer will be a positive number. The squaring basically cancels out any negatives, so our solution set needs to reflect this by including the negative root. In general, whenever you take the square root of both sides of an equation to simplify an exponent, it is plus or minus.(3 votes)

## Video transcript

- [Instructor] What are all the solutions to the equation above? So we have four x squared is equal to 52. Well if we wanna solve for x, we can just divide both sides by four. And then we get x squared is equal to 52 divided by four is 13. So x could be equal to, if
x squared is equal to 13, then that means x could be
the positive or negative square root of 13, so
x is going to be equal to the positive or
negative square root of 13. And you could check your answer. Take positive 13, if you take, or take positive square root of 13. Well, if you square it,
you're gonna get 13. And them multiply it times
four, you're gonna get 52. Take the negative square root of 13, well when you square it,
you're going to get 13, 'cause a negative times
a negative is a positive. And then you multiply it times
four and you're gonna get 52. So x could be negative square root of 13 and/or x could be, or
the two solutions are x is the negative square root of 13 and x is equal to the
positive square root of 13. So that's our choice right over there.