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Find the unknown.$$(x+3)^{2}=-9$$

$$-3 \pm 3 i$$

Algebra

Chapter 0

Reviewing the Basics

Section 2

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

Equations and Inequalities

McMaster University

Harvey Mudd College

Lectures

01:23

Find the unknown.$$(x-…

00:33

Find the unknown.$$x^{…

01:30

02:17

Find the unknown.$$\fr…

02:10

Solve the equation.$$9…

00:47

Solve for the unknown vari…

00:09

Solve.$(x-2)^{\frac{2}…

01:25

Solve for $x$ in.$$9^{…

01:21

01:10

Solve.$$\frac{2}{x^{2}…

03:07

01:07

Find the unknown.$$3 x…

So as we're looking at this X plus three squared problem equals negative nine. What some people might recognize is the very first step to do is to under the square by square, rooting both sides. Um, and some people might actually just prefer that that there's no real solution. Um, and the reason why I'm bringing that to your attention is for you to recognize that the only way to square numbers, uh, if you square negatively get a positive if you square positive if you get a positive so there's no way of getting a real solution for X. But what we learned in this section, or we should already know, is that when you square root a negative, we can put an I an imaginary number of complex number plus or minus, because we could get a positive or negative in the square to nine is three, um, and the plus the square root in the square. Cancel each other out, just left with X Plus three. Um, and at this point, there's only one other thing left to do, and that's to subtract three over. Um, so we get X by itself on the left side, and it's a habit of math, teachers, math people in general to put the whole number or the real part in front of the imaginary part. And you can tell from this answer the correct answer that what we get is a complex solution. So if you were to graph this problem, uh, there would be no X intercepts, or this function would not cross this function. But here's your answer. Negative three plus or minus three I

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