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

Question

Solve each equation in Exercises 65–74 using the quadratic formula. $x^{2} + 8 x + 15 = 0$

Accepted Answer

Hello everyone in this video, we're going to be looking at this practice problem where we're trying to solve for the values of X in the equation X squared plus 20 X plus 96 is equal to zero. So in this case we're gonna be using the quadratic formula which applies to quadratic equations. So recall that the general form for a quadratic equations is a X squared Plus B, X Plus C is equal to zero. And the quadratic formula states that X is equal to negative B plus or minus the square root of B squared minus four times a times C Divided by two. A. So you can see that the quadratic formula gives us a simplified way of finding the values of X when looking at quadratic equations. So if we look at our equation X squared plus 20 X plus 96 is equal to zero. You can see that it follows the quadratic equation standard. So we can try to determine the values of A. B and C in our equation. So in this case you can see that the coefficient in front of X squared is A. And in our equation b coefficient is positive one, so A is equal to one and B is the coefficient in front of the X term. And in our equation that value is 20, So B is equal to 20 And C is just the constant that follows after the X terms. And in this case that constant is 96. So now we've determined the values of a, B and C in our equation. And we can use these values and plug them into the quadratic formula to get the values of X. So if I do that, I have X is equal to negative B. So negative 20 plus or minus the square root of B squared. So 20 squared -4 times a Times one times C, which is 96, Divided by two times a. So two times 1. And from here I can start simplifying. So I have negative 20 plus or minus. The square root of 20 squared is equal to -4 times 96. And that multiplication is equal to Divided by two. So if we simplify the square root We have X is equal to negative 20 plus or - -3, 84 is 16. And that's all divided by two. And notice how the square root of 16 is equal to four. So we can simplify this more by saying X is equal to negative plus or minus four divided by two. And in this case we can start to split the values of X. So notice how we still have the plus or minus. So if we split them we have negative 20-plus divided by two and negative 20 minus four divided by two. So if I simplify these, I have negative 20 plus four, negative 16 divided by two. So that's one of my solutions And - divided by two is -8. And if I look at the second Solution, I have negative 20-4, So negative 24 Divided by two, and that is equal to -12. So I have my two solutions X is equal to negative eight and negative 12. And you can see that that aligns with answer choice D. So hopefully the video helped and see you next time.

Solve each equation in Exercises 65–74 using the quadratic formula. $x^{2} + 8 x + 15 = 0$

Key Concepts

Quadratic Equation

Quadratic Formula

Discriminant

Watch next

Solve each equation in Exercises 65–74 using the quadratic formula. x2+8x+15=0x^2 + 8x + 15 = 0

Key Concepts

Quadratic Equation

Quadratic Formula

Discriminant

Watch next

Solve each equation in Exercises 65–74 using the quadratic formula. $x^{2} + 8 x + 15 = 0$