The Discriminant - Example 4
Liberty University
Solving Quadratic Equationsby Completingthe Square - Example 4


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equation by completing the square. We're gonna do this. Since our first term is nine as the coefficient, we're gonna divide everything by nine so that we can remove that. And so we're left with X squared minus 6/9. We're gonna go ahead and reduce that to to thirds X minus four nights equals zero, and we're gonna go ahead and move our four nights to the other side so that we only have two terms on the left. So we have X squared minus two thirds eggs equals four nights. So the first thing we want to do is our binder be term, which is two thirds, and we want to divide that by one half, which is our multiplied by one half. So that would be to over six, and then we want to square and actually native to over six. So we want to square that. So that's gonna be 4/36 which, actually, I can reduce that even mawr to one nights. So we're gonna add one night to both sides. So I have X squared minus two thirds x plus. One night is gonna equal four nights plus one night. Yeah, so let's simplify that. So we have X squared minus two thirds X plus 1/9 will equal four nights plus 1/9 so square root of one night is one third. So that means we're gonna have X minus one third squared is going to equal five nights. Now the square root of five nights is going to be the square root of 5/3. That's a far as I could get because it is a complex number. So we're gonna have X minus. It's gonna be plus or minus square root of negative five. Over three Children have X minus one third equals square root of 5/3 and X minus one third equals negative square root of five over three. So when I add one third to that, I'm gonna have X equals one plus square root of five over three. It's one solution. Second time gonna add one third again and I'm gonna have X equals one. And this time, because it was the negative minus square root of 5/3. So my solution is gonna be one plus or minus the square root of five over three