Solve each equation using completing the square. See Examples 3 a...

Question

Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10

Accepted Answer

Welcome back, I am so glad you're here. We are given this equation 18 X squared plus X equals four. We are asked to complete the square and then solve for X. The first step for completing the square is we want to see what format our equation is in and this isn't a bit of a modified quadratic equation. We have R A X squared plus B X. And then that is equal to R negative C instead of a X squared plus bx plus C equals zero. And this is a great way to start for completing the square. Next we want to ensure that our A term is equal to one while we look here in our A term, the one in front of the X squared equals 18. So we need to divide that and everything else by 18 to get that equal to one. So 18 X squared divided by 18 will give us our one X squared or just X squared plus for our X divided by 18, that's going to be 1/18 X. And that is equal to and I'm going to keep this as 4/18. So don't need to simplify that yet. Our next step for completing the square is we're going to take what's our B term in front of the X. Here, we're going to take our B term which is 1/18. We're going to divide it by two and then we are going to square it and then that is going to get added to these two spaces here after our B X term and then after our negative, see on the right hand side of the equation. So let's do our work to simplify this. 1/18 divided by two and then squaring it. So we could rewrite this as 1/18 divided by two, Which is the same as 1 18th times 1/2 And 1/18 times 1/ equals 1 36th. We still need to square that. So one squared in the numerator is one 36 squared in the denominator is 1,296. So we are going to add plus one over 1,296 to both sides of this equation. The next step is we are going to factor the left hand side and we have set it up so that this is easily done. It's going to be two of the same factor. We're going to have our X as our first term here and the second term is going to be this be over to that we had from completing the square so it's going to be plus 1 36 in this case. And if we were to foil this thing out, X plus 1 36 times X plus 1 36 it would equal x squared plus 1/18 x plus one over 1296 by design. Alright, we've completed this square now we have to solve for X. We want to combine those terms on the right hand side and we need a common denominator to do that, our common denominator is going to be we will multiply 4/18 times 72/72. In order to get our denominator of in the numerator, four times 72 equals 288. And that's over 1296. That's 18 times 72 plus one over 1296. This will give us 288 plus one in the numerator is 289. That's still over. 1296 will bring down the left hand side, which is the X plus 1 36 squared. Now to get X by itself will take the square root of both sides. And on the left we will have X plus one 36th. And on the right, that will be equal to plus or minus because we're taking the square root. The squared of the numerator, 289 is 17. The square root of the denominator, 1296 is 36. Now we can subtract one 36th from both sides of the equation and we will have X equals on the left, I'll put negative one 36th first and then it will be plus war minus 17 36th. So this gives us two different X answers. We have X equals negative one, 36th plus 17 36th, and we have X equals negative one 36th minus 17 36th. And now because we have a common denominator we can go ahead and add our numerator negative one plus 17 gives us 16 36th and that simplifies to a positive 4/ for the other one. Negative one minus 17 gives us negative 18/36. And that simplifies to a negative one half. There are our two X. Solutions, 4/9 a negative one half. We look at our answer choices and this matches with answer choice. D. Well done, we'll catch you on the next one.

Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10

Key Concepts

Completing the Square

Quadratic Equations

Standard Form of a Quadratic

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