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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.$$(x-4)(x+1)=6$$

$$-2,5$$

Algebra

Chapter 0

Reviewing the Basics

Section 3

Completing the Square

Equations and Inequalities

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

03:15

Solve each of the quadrati…

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In each of the following, …

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02:13

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Okay, so this problem has a few more added steps because what we need to do first is distribute that left side. Um, so I'm talking about distributing X into the problems. We're looking at X squared plus one X, but then also distribute that negative four to each terms of minus four X minus four. That's native four times one. Because now what I need to do is combine like terms. So we're looking at X squared minus three X. What I'm also going to do is, uh, pull blank right here and a blank on this side, and I'm going to add this forward to the right side, so we're gonna get 10. So now what I can do is I can complete the square like they asked me to. Is just taking this middle number divided by two. You always divide by two and square it well as you square Negative. First of all, you get a positive. Three squared is 92 squared is four. So the only way to add nine force to both sides and if you also to one side is to add it to the other side. Um so as I'm looking at this. Now the left side is a perfect square China mule, and I can reduce it to, um, factors and nine force that had to be negative. Three. It's always this number X minus. Three halves X minus three Have so X minus three have squared on the right side. That would change 10 to be 40. Force 40 divided by four is 10. And what I'm doing is getting the same denominator so I can add and get 49 force so the denominators are the same. So now I can solve the square problem by square, rooting both sides and on the left side, your square root in the square cancels. You're left with X minus three halves. On the right side, you get plus or minus square to 49 7 square root of forest, too. Well, now I can solve this by adding three halves over. What's nice about adding three halves over is the denominators are already the same, so I can actually reduce this 21 answer would be 10 halves has three plus seven, and the dynamic stays the same in three minus seven will be negative four halves. So the two correct answers for X would be positive. 5 10 2 by two and negative 2 to 4. Divide by two, so, yeah.

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