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Find the unknown.$$(3 x-5)^{2}+18=0$$

$$\frac{5 \pm 3 \sqrt{2} i}{3}$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

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

Equations and Inequalities

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

01:57

Find the unknown.$$(3 …

01:24

Find the unknown.$$(x+…

01:45

Find the unknown.$$(5 …

01:06

Find the unknown.$$x^{…

01:44

02:31

Solve the equation.$$0…

03:17

02:12

01:04

Solve.$$3 x^{2}+5 x-10…

01:00

Find the unknown.$$5 x…

01:19

Find the value of $3 x^{2}…

00:22

Find the value of $x$$…

this problem is asking us to solve for X three X minus five. Squared plus 18 is equal to zero. Mhm. Uh, yeah. So as I'm looking at this, you got to get this squared piece by itself. So your first step would be to subtract that 18 over, um, and zero minus 18 is negative 18. And the quick answer, uh is that a quick mention is that you're going to get a non real answer because it's impossible to square a real number and get a negative. Um, you know, and but we can fix that because if I ask you to square root that piece we can do plus or minus, we can pull an eye in front. Um, so if I were to look at that, you might rewrite that as I times the square to nine Times Square to to it might be curious why I chose the number nine is That's a perfect square. And I know the square to nine is three. Group two. I know other teachers showed this other work. Where they break it down is nine and two and then three and three, so a pair of threes get pulled in front and then your leftovers that don't have a pair go under the radical. But we do that because the square in the square cancel each other out and we're almost there. We're almost ready to finish solving for X. Uh, we just have to solve for X by adding five over and because five is a real number and the three I wrote to is not, we cannot put them together. And it's a habit of Matthew to put the real part in front of the imaginary Uh, And then one more thing is to solve a multiplication problem multiplied by three. We would divide by three, and this is a good enough to answer. I do want to point out, though, that this complex answer some people might prefer writing it as breaking each piece up. I've divided by three, and the reason why this might be beneficial as three Divide by three would cancel each other out. So this is a pretty nice answer as well. That is equipment, um, to what's up here?

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