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Find the unknown.$$(4 x-7)^{2}=18$$

$$\frac{7 \pm 3 \sqrt{2}}{4}$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

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

Equations and Inequalities

Missouri State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:10

Find the unknown.$$\fr…

00:32

Find the unknown.$$x^{…

01:09

Find the unknown.$$17 …

00:42

Evaluate the following.

00:10

Evaluate.$$7^{2}-3…

00:25

If $4^{x}=7,$ what does $4…

00:55

So as we look at four x minus seven, squared is equal to 18. It's important that you recognize that the squared gets undone by square root in both sides. Um, and there's a lot of different ways that teachers explain how to get, you know, 18 broken down with a pair of threes. It doesn't matter how you break it down. You're going to get two threes and two, and you put the pears in front. Uh, now other teachers have other ways of explaining this. Like they rewrite 18 as Route nine times route to, and then the square root of nine is equal to three. And don't forget about plus or minus. Um, so, however, your teacher explains it, I would encourage you to do the problem that way. But now we're ready to simplify this because it's the same steps and a lot of teachers are okay, because if you add seven over, uh, it's impossible to simplify seven plus or minus three route to at this other side. Um, so that's why it's perfectly fine on this problem to leave them as one statement and then your last step to solve for X is to divide that for over all over four. Um, yeah. So this is a perfect answer just for reference. Sometimes teachers will split this up and write a seven force if you divide every piece, like three to all over four. But it's important that you realize you cannot simplify this because two is under the radical and four is a whole number. So here's another acceptable answer. If you wanted another one, hang up.

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