Solve each equation using the quadratic formula.

Question

2 x^{2} = 3 - 4 x

Accepted Answer

Hello today we're gonna be solving a quadratic equation by using the quadratic formula. So the quadratic equation given to us is four X squared equal to negative one plus seven X. Now since we're asked to solve this equation we need we need to go ahead and set the equation equal to zero. In order to do that. I'm going to subtract seven X to both sides of this equation and I'm going to add one to both sides of this equation. Doing so is going to give me four X squared minus seven X plus one is equal to zero. So now we need to go ahead and use the quadratic equation. Let's go ahead and recall what the quadratic equation is. So the quadratic equation states that if we have a trine Amiel in the form of a X squared plus bx plus c equal to zero. We take our A B and C and X is going to equal to negative B plus or minus the square root of B squared minus four times a times C. All of that over two times 8. So we need to go ahead and identify what are a B and C are going to be for this trin Amiel? Well A is just the coefficient in front of our x square term. So A is going to equal to four, B. is the coefficient in front of our x term. So B is going to be equal to negative seven and C is just the constant at the end of the tri no meal so C is going equal to one. So let's go ahead and take our A B and C and plug it into the quadratic equation. Doing so is going to give me X. Is equal to negative negative seven plus or minus the square root of negative seven squared minus four times four times one. All of that over two times four. And I'm gonna go ahead and continue this over here but we just need to go ahead and simplify a little first. So negative negative seven is gonna give me positive seven and that's gonna be plus or minus the square root of negative seven squared which is 49 - times four, which is 16 times one, which is still 16 And all of that is going to be over two times four which is eight. And just to simplify even further, 49 minus 16 is gonna give me the value of 33 so currently X is equal to seven plus or minus the square root of 33/8. Now 33 is a prime number is not prime number but it produces a product of prime numbers that cannot be simplified any further. So this is going to be the simplest form of our solution which means that our solution is going to be a so I hope this video helps you in applying the quadratic equation and I'll go ahead and see you all in the next video

Solve each equation using the quadratic formula. $2 x^{2} = 3 - 4 x$

Key Concepts

Quadratic Equation Standard Form

Quadratic Formula

Discriminant and Nature of Roots

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