Solve each equation. (x+4)(x+2) = 2x

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Hello, today we're going to be solving the quadratic equation. So what we are given is the quantity X plus three times the quantity X plus six is equal to three X. Now, in order to solve for X, we need to foil the left hand side. In order to foil the left hand side, we're going to multiply X with X and X with six. And that is going to give us X squared plus six X. Then we're going to multiply positive three with X and positive three with positive six. And that is going to give us positive three X plus 18 and that is going equal to three X. Now, on the left hand side, we're going to combine the like terms together which is six X and three X. And that is going to give us X squared plus nine, X plus 18 is equal to three X. Next, since we want to solve for X, we want to set this equation equal to zero. And in order to do that, we're going to subtract three X to both sides of the equation that is going to give us X squared plus six X plus 18 is equal to zero. And in order to solve this Trina meal, we're going to use the quadratic equation. Now, the quadratic equation states that 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. And this is where A B and C are going to be the coefficients of your given Trina meal for the tri no meal or for the equation given to us here, the coefficient of the first term is going to be one. So A is equal to one B is going to be the coefficient of the second term, which in this case is going to be positive six and C is going to be the constant, which is going to be 18. So if we plug this into the quadratic equation, what we are left with is X is equal to negative B which is negative six plus or minus the square root of B squared, which is negative six squared times four times A which is one Times C which is 18 All over two times a which is two times 1. Now let's go ahead and simplify the numerator in the square root. Negative six squared is going to give us 36 negative four times one times 18 is going to give us 72. So we have negative six plus or minus the square root of 36 minus 72. All over two times one, which is going to give us two. Now, in the square root, 36 minus 72 is going to give us negative 36. So we have negative six plus or minus the square root of negative 36/2. Now, there's one thing to note here, we have a negative number inside of a square root. And whenever you have a negative number inside of a square root, you can represent the negative as the imaginary value. I, so we can rewrite the given numerator as negative six plus or minus the square root of 36 I all of that divided by two. And so what that means is that we're going to have a complex solution for this problem. Now, the square root of 36 can be simplified to just six. So we have negative six plus or -6 I all divided by two. And in the numerator, since both of the terms have the value of six, we can factor out of six to give us six times negative one plus or minus I divided by two And 6/2 is going to reduce to give us three. So we have three times negative one plus or minus I. And now we can go ahead and redistribute negative three into this quantity. And that is going to give us negative three plus or minus three I. Now, since this is a plus or minus statement, we can go ahead and separate this into two equations that is going to give us X is equal to negative three plus three, I and X is equal to negative three minus three. I. Now there's no way to simplify these statements any further. So what we have is too complex solutions for X and with that being said, the answer to this problem is going to be be. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Solve each equation. (x+4)(x+2) = 2x

Key Concepts

Expanding Algebraic Expressions

Setting the Equation to Zero

Solving Quadratic Equations

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