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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.$$(x-3)(x+5)=20$$

$$-7,5$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

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Solve each of the quadrati…

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In each of the following, …

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So we have a quadratic. It doesn't quite look like a quadratic yet. And to solve this by doing the completing the square, you have to certify distributing the X in there. So we're looking at X Square plus five X and also distribute the negative three in there. Negative three x and they have three times five is negative. 15. I'm gonna leave that 20 alone because now what I need to do is combine like terms. So I have X squared plus two X. I'm just gonna leave a blank right now in a blank over here, because now what I need to do is add 15 to the right side. 20 plus 15 is 35 and now I can complete the square, which is taking this middle number two. You always divide by two and then you square that number will to divide by 21 square. It is one, so I can add one. Now, the only way to add 1 to 1 side is if I also add one to the right side. So now what I can do is I can combine these together many factors of one that had to be too Um, and here's a shortcut. It's always this number X plus one X plus one so I can write X plus one squared 35 plus one is 36. So now I'm ready to solve a square planned by square rooting both sides square root mean square will cancel so much with X. Plus one equals positive and negative. Six. Because we can square a negative number to get positive. 36. So your last step would be to subtract one over and might help you think about it as six minus one to give you five as one answer or negative six minus one to give you negative. Seven as an answer. Um, so the two values for X could be negative seven and positive five.

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