About this video
The instructor solves 4x² = 52 by dividing both sides by 4 to get x² = 13. From there x can be either the positive or the negative square root of 13. The video then checks both answers by squaring them and multiplying by 4, which returns 52 each time.
You'll be able to
- isolate a squared variable by dividing both sides of an equation by its coefficient.
- explain why an equation of the form x² = a positive number has two solutions.
- check a solution by substituting it back into the original equation.
Key words
- Square root
- A number that, multiplied by itself, gives the original number, such as √13 for 13.
- Solution set
- All the values that make an equation true, which for x² = 13 is both the positive and negative square root of 13.
- Coefficient
- The number multiplying a variable, such as the 4 in 4x².
- Inverse operation
- An operation that undoes another, such as dividing by 4 to undo multiplying by 4.
- Checking an answer
- Substituting a proposed solution back into the original equation to confirm it makes the equation true.
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.
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