Exercises 82–84 will help you prepare for the material covered in...

Question

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x^2+4x−1=0

Accepted Answer

hey everyone here are asked to solve the equation, X squared plus six. X plus two is equal to zero. And so first before we start solving for X we want to recall the standard quadratic equation which is a X squared plus Bx plus plus C. Is equal to zero. And now from here we want to find our A. B. And C values from the given equation. So we can see that our A. Is equal to one, B is equal to six and C is equal to two. And now from here we can start solving for X. But we need to recall the quadratic formula which tells us that X is equal to negative B plus or minus the square root of B squared minus four A. C. All divided by two. A. And now from here we can just plug in our A. B. And C values and start solving for X. So we have negative B which will be six. So we have negative six plus or minus the square root of B squared which will be six squared minus four times A. Which is one times C which is two, all divided by two times A which is one. And now we can just continue to simplify. So we have X is equal to negative six plus or minus. The square root of six squared is 36 minus four times one times two is eight, all divided by 282 times A which is two times one. So we just have to and now further simplifying, we have negative six plus or minus the square root of 36 minus eight gives us 28 all divided by two. And now we need to further simplify this square root. So if we take this square root of 28 we can rewrite it as the square root of four times seven. We know that the square root of four is two. So this square root simplifies to two times the square root of seven. So in putting this information into our equation above we have negative six plus or minus two times the square root of seven, all divided by two. And now we can see that both terms can be divided by two. So we get negative three plus or minus the square root of seven and therefore we know that we have two values for X. So X can be equal to negative three plus the square root of seven or negative three minus the square root of seven. And this leaves us with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time

Struggling with College Algebra?

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x^2+4x−1=0

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