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In $9-26,$ solve each quadratic equation by completing the square. Express the answer in simplest radical form.$$2 x^{2}-6 x+3=0$$

$\frac{3+2 \sqrt{3}}{3}$ and $\frac{3-2 \sqrt{3}}{3}$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 1

Real Roots of a Quadratic Equation

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

03:06

In $9-26,$ solve each quad…

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04:44

03:39

01:58

02:34

02:01

04:27

01:54

So I hear we have a function to X squared minus six X plus three this equal to zero in order to use completing the square. Let's start off by factoring this out right, you can't. It's hard to do this if you have a, um, a co option of two in the X squared. So it's factor this two out. And if you factored to Alec, you can also factor two out of the six negative six x so it will become two times X squared, minus three X. Keep the three out of it for now. Thank you, Thank you. Now, if you take a look at this native free X, this is technically the second term of and expressed form or expanded form of apologetic expression, and you could use the roots Negative three halves number three house times two people, native three. So let's get this room handy. Red pen over here. Let's pretend we use X minus three halves squared. So what would occur if we would get two times X squared? I'm gonna write this expense. We have squared and expanded form. Just concede a little more clearly. X squared minus three X and then three have some students. We need this final term that is equal to nine forts, correct. So it's at night worths, all right, red pen. And we also have to subtract 9/4. But since we don't want to interfere with this nice little expression, you got going on the parentheses because it's it'll be clean to just simplify like that. Well, multiply that negative nine forts by two. So will become negative nine haves and leave it out of there so you can actually simplify this X squared minus three hacks plus 9/4 R X squared minus three X plus nine for it's a little Easier. So let's do that. Let's it's untracked nine haves and keep it on the outside and then once again at that three from before and we would get that school gets two times X minus three halves squared not to add the equal zero. Originally, colleges that you get two times X minus three zero X rays. Three Scored the expense we have squared. That's not very clear, but remember, that's just a negative two halves right there. Tim's excited. You have squared, um, native nine halves, plus the results of six hands so it would be minus three. Have negative naps plus six absence. Major three has men. That was a zero just lining up the science of clarity. And then what we would that have to do is solve for X right. You want to find X in its simplest form. So we would get two plums. X ministry have squared. Been that native three halves over. You have the right side. Then you have x three have squared. It was three halves divided by to correct. So three warrants then square both sides. You get X equals Dr Emmett experience. They have equals. We have not moved three halves already, and we have first you if you'd say X minus three has because plus or minus root of 3/4 and therefore X equals closer minus root 3/4 plus three hands and that is it. That is X we're solving for X that is using competing square. And initially we had a lot of factoring you do, and this is a little trickier than if you had a coefficient of one, but that whenever you see a coefficient that it's not one you'd have to know to back here. Now what's it

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