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+6=0

Accepted Answer

Hey everyone here we are asked to solve the equation, X squared plus six. X plus 11 is equal to zero. Now before we can start solving for X we need to recall the standard quadratic equation which is a. X squared plus B. X plus C is equal 20. And now we need to identify our A B and C values. So our coefficient of X squared which is A. Is one from our giving equation and then B is six. And we can see that C. Is then 11. And now from here we need to recall the quadratic formula so we can solve for X. So the quadratic formula is X is equal to negative B plus or minus the square root of B squared minus four A. C. All divided by two A. Now from here we can just substitute in our found values. So we have our negative B which would be negative six plus or minus the square root of B squared or six squared minus four times A. Which is one times C which is 11, all divided by two times A, which would be two times one. And now we can just start simplifying So we see that X is equal to negative six plus or minus. The square root of six squared is minus four times one times 11 which is 44 all divided by two times one which is just two. And now simplifying the square root further we have negative six plus or minus the square root of 36 minus 44 gives us negative eight. Again all divided by two. And now if we take a look at this square root of negative eight we need to simplify it further. But when you take the square root of a negative you need to incorporate I so if we recall I squared is equal to negative one. So this square root of negative eight can become the square root of eight I squared. And now from here we know that eight is the same as four times two. So we have four times two times I squared and we know the square root of four would be two. And then the square root of I squared is just I. So we have to I times the square root of two which is again equivalent to this square root of negative eight. And now we can incur cooperate this simplification into our original equation. So we now have negative six plus or minus two. I times the square root of two. All divided by two. And now we can just simplify further by dividing both terms by two. So we actually have X is equal to negative three plus or minus I times the square root of two. And so because of this plus or minus we can see that X is equal to negative three plus I times square root of two or negative three minus I times the square root of two. And this leaves us with answer choice C thanks for watching. I hope you found this video helpful and I'll see you again next time.

Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x^2+4x+6=0

Key Concepts

Quadratic Equations

The Quadratic Formula

Completing the Square