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Complete the square in each of the following by putting in the form $(x+B)^{2}-C$$$x^{2}+5 x$$

$$(x+5 / 2)^{2}-25 / 4$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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Complete the square in eac…

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Complete the square. $…

Complete the square for ea…

To complete the square of …

this problem is looking at X squared plus five X and what our goal loses it. Take it from this form. I'm just going to call it D X. I know that's kind of weird, but what we have to do is change it to X plus a different number squared, plus a third. Yeah, third number. Um, now I do realize that the directions that they want me to write minus it will make sense when we get to it. Why? It's minus, um, and it's always the same process. You always take this number. That's why its called Completing the Square is. What you're doing is you're taking that number and divide it by two. And when you square it that's completing the square. What will happen is, uh, you'll come up with a perfect square, try no meal, and that's why it's the same process, no matter what. Uh, now the square of Fraction. I don't know if that's a struggle for you. You just multiply by itself and to multiply fractions. It's just straight across. Five times five is 25 two times two is four. So what we're gonna do is take that term. You know what we started with, and we're going to add that 25 force now. You cannot just add any number in a problem because that changes the value. So what I'm going to do is also subtract off 25 force, because by adding the same number and later subtracting, really, I'm not changing the value of that X squared plus five X. And that's why this is part of your process and how you complete the square and the whole reason for doing that because we want factors of 25 force that had to be five sort of factoring this perfect score China view. And it's always this number. It's always whatever. That middle number, divided by two, is five house plus five halves is five and five has times five houses, always 25 fours. So how do we write our answer instead of writing? X Plus five has twice we can write at once squared. And don't forget about this piece either. And there's your final answer. Hopefully, that all made sense

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