Solve each equation in Exercises 65–74 using the quadratic formul...

Question

Solve each equation in Exercises 65–74 using the quadratic formula.x^2 + 5x + 3 = 0

Accepted Answer

Hello everyone in this video we're gonna be looking at this practice problem where we want to find the value of X in the equation X squared plus 11 X plus one. So in this case you can see that the equation follows the general form for a quadratic equation of a X squared plus bx plus C equals zero. And using the quadratic formula is a simplified way of finding the values of X. Recall that the quadratic formula is X is equal to negative B plus or minus the square root of B squared minus four times a times C, Divided by two times a. So in this case if we look at the general forum for the quadratic equations and we look at the equation that were given X squared plus 11, X plus one equals zero. We can define values for a B and C from our equation. So you can see that A is equal to one because the x squared component has no coefficient. And you can see that B is equal to because that's the coefficient in front of the X term and see Is equal to one. So now we've defined a B and C in terms of our equation and we can plug in these values into the quadratic formula. So if we do that, the quadratic formula becomes X is equal to negative B. So negative 11 plus or minus the square root of B squared 11 squared minus four times A. Which is one and C which is also one That's divided by two times a. So two times 1. So if we simplify, We got X is equal to negative 11 bluster minus the square root of 11 squared is 121 and four times one is four and four times one again is still four. So we're left with negative four And that's divided by two. So if we simplify the square root we're left with X is equal to negative plus or minus the square root of 117, divided by two. So if we take a closer look at the square root, we have 117. So let's try to find factors that we can pull out of the square root. So three times 39 is equal to 1 17. But if I factor these out, I won't be able to pull anything out of the square root. So if we take it further nine times notice how nine is the same as three squared. So if I factor out a nine, I can take out three from the square. So I can rewrite my equation as X is equal to negative 11 plus or minus. Going to factor out the nine Square root of nine times square root of divided by two. So now The square root of nine is three. So I can rewrite my equation as X is equal to negative 11 Plus or -3 Times The Square Root of Divided by two. And now you can see, I've simplified the quadratic equation as much as I can. So this becomes my final answer and notice how there's still a plus or minus. So there's actually two solutions for X. X. Is equal to negative 11 plus three times the square root of divided by two, And it's also negative 11 -3 times the square root of 13 divided by two. And if you look at the answer choices, you can see that answer choice B aligns with this too, notice how A. Is very similar but A. Has this Positive 11 instead of negative so make sure to be careful when choosing answers. But hopefully this video helped and see you next time.

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Solve each equation in Exercises 65–74 using the quadratic formula.x^2 + 5x + 3 = 0

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