Solve each equation in Exercises 83–108 by the method of your cho...

Question

Solve each equation in Exercises 83–108 by the method of your choice.

(2x + 3)(x + 4) = 1

Accepted Answer

Hello today we're going to be solving this equation using any of our preferred methods. So the equation given to us is the quantity three X plus one times the quantity X plus two equal to four. Now, since we want to go ahead and solve for X we need to set this equation equal to zero. And in order to do that we're going to go ahead and foil the left hand side together, foiling is going to give me three X squared plus six X plus X plus two is equal to four and I'm gonna go ahead and combine our like terms which is six X and X. So this is going to give me three X squared plus seven X plus two is equal to four. Now in order to set this equation equal to zero, I'm going to subtract four from both sides of the equation and doing so is going to give me three X squared plus seven X minus two is equal to zero. Now this is not a fact arable. Try no meal. So how can we solve for X? If this is not fact, herbal while we can go ahead and use the quadratic equation and the quadratic equation is X is equal to negative B plus or minus the square root of B squared minus four times a times C. All over two times A. Now abc are going to be the leading coefficients in your given try no meal. So for our try no meal here, A is going to be the coefficient in front of the X squared term. So A is equal to three, B is going to be the coefficient in front of the X term, so B is equal to seven and C is gonna be the constant at the end, which in this case is negative two. Now we're just gonna go ahead and plug this into the quadratic equation. Doing so is going to give me X is equal to negative B which is negative seven plus or minus the square root of seven squared minus four times A which is three times C, which is negative two, All of that over two times a which is two times three. Now we need to go ahead and simplify seven squared is going to give me 49 negative four times three times negative two is going to give me positive 24. So what we have is X is equal to negative seven plus or minus the square root of 49 plus All over two times 3, which is six now 49 plus, 24 is going to give me the value of 73 so X is equal to negative seven plus or minus the square root of 73/ and 73 is a prime number. So we can go ahead and leave the square root as is so this is gonna be the simplified version of X. So the only thing we can really do is just go ahead and split up X since this is a plus or minus quantity, so doing so is going to give me X is equal to negative seven plus the square root of 73/6 and X is equal to negative seven minus the square root of 73/6. And this is going to be the solution to our equation. And with that being said, the solution to this problem is going to be a So I hope this video helps you in understanding how to solve this type of equation and I'll go ahead and see you all in the next video.

Solve each equation in Exercises 83–108 by the method of your choice. (2x + 3)(x + 4) = 1

Key Concepts

Factoring

Zero Product Property

Isolating the Variable

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