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Solve each of the quadratics by first completing the square. When the roots are irrational, also give the solutions to the nearest one thousandth.$$4 x^{2}-5 x+8=0$$

$$\frac{5 \pm \sqrt{103 i}}{8}$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

02:23

Solve each of the quadrati…

02:13

02:50

01:23

In each of the following, …

02:25

02:20

02:36

02:12

03:15

02:52

02:38

02:06

02:19

02:01

01:46

01:13

01:11

01:07

02:27

we have this quadratic for X squared minus five X plus eight equals zero. If we're gonna solve by completing the square, you want this leading coefficient equal one which I can fix by dividing everything by four. So now I'm left with X square. Now I like fractions. So I'm going to leave this as five Force X uh, and I'm going to recognize that eight divided by forest, too. So what I do is I like to leave this alone except want me into a Subtract that to the other side. So now it looks easier for me to work with with completing the square in the process is always taking half of that be value, so some people divide by two. But I like to multiply by one half with these fractions, So it's easier for me to recognize that that's native five eights when I square that a negative squared is positive. 25/64. So now what I can do is I can look at that left side and say, Oh, that's a perfect square China meal. That's why we do this process and there's a shortcut. It's always this value. That's why we go through that process X minus 58 squared and maybe over here changed that to be, uh, that negative two to be negative, 128 over 64. So then adding 25 2. That's a little bit easier. It's negative 103 over 64. I don't know if that really is easier for anybody, but now we have this square problem that's pretty straightforward to solve you under the square by square, rooting both sides and you square refraction by doing each piece individually. So looking at X minus five eights, we anytime you square root when you're solving of a plus or minus, we can only square root of negative. If we have an imaginary results. It's the only way to get that. The square to 64 is eight, and now the problem is pretty easy because we have the same denominator and all I have to do is add 5/8 to the other side, and with the denominator being the same, we can just write it all over eight. And there's your complex solution, all of them mhm

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