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

Question

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

4x^2 = 2x + 7

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to solve the value of X. In the equation two x squared minus x minus 11 equals zero. In this case the equation follows the form of a quadratic equation where a X squared plus bx plus C equals zero. That's the general form for a quadratic equation. And the quadratic formula gives us a simplified way of solving for X where 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 if I look at the general form of a quadratic equation and I look at the equation that we are trying to solve, we can pull values or substituting values of A B. And C. From our equation into the quadratic equation. So you can see that a. And the equation is equal to two B. Is equal to -1. Notice how when we're substituting, we have to make sure that the values here align. So at first glance it may seem like the value of B is one, But because we have a negative instead of the positive, the value is actually negative one And in the same way C is equal to -11. So now that we defined all the values for a B. And C. From our equation we can plug that those values into the quadratic equation. So X is equal to negative B. And in this case B is equal to negative one plus or minus the square root of B squared. So negative one squared minus four times a times two time C. Negative 11 Divided by two times a or two times 2. So you can see I plugged in all the values for a B and C. So if I solve this I have X is equal to one plus or minus. The square root -1 Squared is positive one -4 times two is negative eight times negative Divided by two times 2, four. And then if I continue solving I have X is equal to One plus or minus the square root of one, negative eight times negative 11 is positive divided by four. So simplifying the square root One step further, I have x is equal to one plus or minus the square root of 89 divided by four. So in this case 89 is a prime factor. So we can't factor it into anything. So the square root will stay as the square root of 89. So you can see that we actually have two solutions when solving the quadratic equation or this quadratic equation in particular because of the plus or minus. So X is equal to one plus the square root of 89 divided by four And it's equal to 1 - the square root of divided by four. And you can see that this aligns with answer choice A. So hopefully this video helped and see you next time

Solve each equation in Exercises 65–74 using the quadratic formula. 4x^2 = 2x + 7

Key Concepts

Quadratic Equations

Quadratic Formula

Standard Form of a Quadratic Equation

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