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

Question

Solve each equation using completing the square. See Examples 3 and 4. x^2 - 2x - 2 = 0

Accepted Answer

Welcome back. I am so glad you're here. We are given this equation M squared minus four. M minus one equals zero. We are asked to complete the square and then solve for m. Alright. The first step here, we're going to take a look and see what format our equation is in and that's in a pretty standard quadratic equation. Form A X squared plus bx plus C equals zero. Which is a good place to start. The next thing we want to do is make sure that our A term equals one and it does in front of this M squared. That's a one. So great. We're in good shape for that. Next we want to bring our C term to the other side of the equal sign. So we'll have a X squared plus bx and then we'll leave a space where the sea was. That'll equal negative C. And then we'll leave another space after that negative see on the right hand side. So in this case we'll be adding one to both sides. That's R. C. Term, bringing that over to the right and we'll have M squared minus four. M. Leaving a space equals positive one. And leaving a space after that. Next we're going to be filling in that space. And what we're filling it in with is B. R. B. Here in front of the M. That's negative four Divided by two. So -4 divided by two all squared. So let's simplify that. Inside the parentheses simplifying that first negative four divided by two is going to be a negative two and negative two squared equals a positive four. So we're going to be adding plus four to both of these two spaces. What we do to one side, we need to do to the other. Next we are going to be factoring the left hand side and that is all set up for us, We are going to be putting this in, the format will take this M squared, will be r. M and then that will be plus this, be over to that we have in parentheses here or this negative two in this case and that if we were to foil this whole thing out m minus two, I'll change that plus minus two. M minus two times. M minus two would give us this M squared minus four. M plus four that we had before by design that's completing the square and on the right hand side that is equal to five. Alright, now let's solve for m we finished completing the square, we'll solve for m we're going to take the square root of both sides to get rid of that squared On the left. So on the left we have m minus two and that's equal to because we're taking the square root of five, that's going to be plus or minus the square root of five, we can't simplify the square root of five. So we leave that as is we can add two to both sides. And so on the left we have em by itself equals yea, we have a positive too, plus or minus the square root of five. And we can write this as two answers. M equals two plus the square root of five, and M equals two minus the square root of five. And there is our answer, we look at our answer choices for a two plus the square to five and two minus the square to five. And that 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. x^2 - 2x - 2 = 0

Key Concepts

Completing the Square

Quadratic Equations

Perfect Square Trinomial

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