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Find the unknown.$$\frac{5}{6} w^{2}-\frac{1}{4}=\frac{5}{3}$$

$$\frac{\pm \sqrt{230}}{10}$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

Solving Equations of the Form $a x^{2}-b=0$

Equations and Inequalities

Campbell University

McMaster University

University of Michigan - Ann Arbor

Lectures

02:48

Find the unknown.$$\fr…

03:22

01:05

Find the unknown.$$6 w…

01:40

04:36

Solve for the unknown, and…

09:54

09:06

00:34

Evaluate the expression fo…

05:42

01:52

Evaluate.$\frac{5}{12}…

02:01

Perform the indicated oper…

Simplify each expression.<…

01:50

Subtract.$$\left(\…

01:01

Solve each equation.$$…

00:24

00:18

we're looking at solving for this unknown, which is W in this problem. Oops, it's on fourth equals five thirds. Uh, now there's a lot of different things. You can do this, but my experience. Most students do not like the fraction, so you can find the least common multiple between 6 to 4 and the three and multiply by both sides of the equation by that number, which is acceptable. So as you think about it, you know, 12 is a multiple 64 12 is a multiple four and 12 is a multiple of three. So as I distribute that and multiply it in, we can get an easier problem to work with because 12, divided by six, is two times five is 10 12, divided by four is three times one is still three 12, divided by three. It's four times five is 20. So that's how I do that math in my head. Um, otherwise, you can do this with a calculator. You can even add the fractions if you really want, because now your goal should be to get w by itself will start by adding three over. So we're looking at 10 w squared on the left side equals 23 before square rooting. You want to get the 10 over by dividing that, and then you can square root both sides. And here's the thing is, some teachers will let you leave your answer for W as plus or minus that giant fraction. But most teachers don't let you leave the radical in the denominator. So what you can do to fix as multiply top and bottom by Route 10, And the reason why this works is we're technically multiplying by one. So we're not changing the value of that. We get the square root of 230 in the numerator and then the square root of 100 the denominator you saw that plus or minus. The reason why that is what you want is because we know the squared of 100 is 10 mhm. We can leave that as route to 30 because that does not break down at all. That's as best as you can do. It's 23 is a prime number and 10 breaks down to two prime numbers that are not 23. So that's it. This is your final answer for W

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