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Find the unknown.$$(3 x-2)^{2}+25=0$$

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

Algebra

Chapter 0

Reviewing the Basics

Section 2

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

Equations and Inequalities

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:06

Find the unknown.$$x^{…

01:24

Find the unknown.$$(x+…

00:42

01:07

Find the unknown.$$3 x…

02:16

Find the unknown.$$(3 …

01:45

Find the unknown.$$(5 …

01:00

Find the unknown.$$5 x…

02:17

Find the unknown.$$\fr…

00:56

00:21

Solve.$x^{2}+25=0$

01:44

01:42

Solve.

$$2 x^{…

00:38

Solve each equation.$$…

01:23

Find the unknown.$$(x-…

0:00

So we need to solve for X in this problem. Three X minus two squared plus 25 is equal to zero. Uh, So what I need to do is get this squared piece all by itself, and that can be done by subtracting this 25 to the right side. So what I have is zero minus 25 is negative 25 and I have the three x minus two squared by itself. Now, the quick answer is that this is impossible, that we are not getting a real answer. Um, and the reason for that is because no matter what X is whether we're squaring a positive squaring and negative, we can only get positive answers. If this are a real solution, however, we can undo the square by square, rooting both sides. We can write out that we're square rooting and negative by this imaginary part. We need to answers plus minus. And we know the square to 25 is five. Um, yeah. So that's your clue that you have an imaginary or it's actually called a complex solution when we get to this, because our next step is to add to over Since two is a real number. We can't combine it with this imaginary. So we right in front of the habit of math teachers as we write the real part in front of the imaginary. And then your last step is to divide everything by two to start at 93 plus reminds five I all over three to get X by itself. And there's your answer. Uh, just for the record, some math teachers like writing the answer this way, but it's all preference. Uh huh. But there's your complex solution, as I predicted.

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