Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = ...

Question

Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = 8

Accepted Answer

Hello. Today we're going to factor a quadratic equation. So the equation given to us is eight X squared plus two X equal to 15. Now in order to factor this this needs to be in the form of a try no meal. So in order to get a try no meal let's go ahead and subtract 15 both sides of this equation. Doing so is going to leave me with eight X squared plus two X minus 15 equal to zero. Now in order to start factoring this, let's go ahead and consider the factors of the first term and last term. So the factors of eight are going to be 124 and eight And the factors of 15 are going to be 1, 3, 5 and 15. Now when we're picking factors all these factors could potentially be positive or negative. So let's think about two numbers that can multiply together together to give us eight X squared. Well those two numbers are going to be four X and two X. So four X and two X. Multiply together to give us eight X square. So we know that's going to work now we just need to go ahead and pick two factories of 15 that can potentially foil together to give us the original trin Amiel Let's go ahead and choose negative five and positive three. Now we need to check to see if these two mono meals give us the original Try no meal. So let's go ahead and foil them together. So currently we have four X minus five times two X plus three in order to foil this, we're gonna multiply four X 22 X. Doing so is going to give me eight X squared. Next we go ahead and multiply four X to positive three. That's going to give me positive 12 X. Next we're going to multiply negative 5 to 2 X which gives us negative X. And finally we're gonna multiply negative 5 to positive three which gives us -15. Now to simplify this we're just gonna go ahead and combine like terms 12 x minus 10 X. Is going to leave me with two X. So we then have eight X squared plus two X minus 15. So this trin Amiel matches our original try no meal which means that four x minus five times two X plus three is the factored version of this. Try no meal now that we know that this is the factor version. We need to go ahead and sulfur X. Since both of these quantities are equal to zero, we're gonna separate this into two separate equations. We're going to have four x minus five equal to zero and two X plus three equal to zero. Now we need to solve for X for both of these for the left hand side, all we're gonna do is go ahead and add five to both sides of the equation. Doing so is going to leave me with four X equal to five. And finally what I want to do is divide everything by four to get X by itself, and that's going to give me X is equal to 5/4, which is one of our solutions. Now, we need to go ahead and solve the right hand side in order to solve the right hand side. I'm just gonna go ahead and subtract three to both sides of the equation. Doing so is gonna leave me with two. X is equal to negative three, and finally I'm gonna divide everything by two, which then leaves me with X equal to negative 3/2. And that's gonna be our second solution to this equation. So the solutions to this equation is X is equal to 5/4 and X is equal to negative 3/2. That means that the overall solution to this problem is going to be C. So I hope this video helps you understand how to solve the quadratic equation by factoring and I'll go ahead and see you all in the next video.

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