Solve each quadratic equation using the quadratic formula. See...

Question

Solve each quadratic equation using the quadratic formula. See Example 7. x² - 2x - 2 = 0

Accepted Answer

Welcome back everyone. In this problem, we want to use the quadratic formula to solve the quadratic equation. P squared minus 10 P plus 22 equals zero. For our answer choices A is the square root of three plus or minus five. B is the five plus or minus the square root of three C is three plus R minus a square of five and D is a square of five plus or minus three. Now, what do we know? Well, we want to use the quadratic formula to solve the quadratic equation and in our equation P squared minus 10 P plus 22 it's written in the general form. Now recall that for a quadratic formula, it says that for a quadratic equation in general form AX squared plus BX plus C equals zero, then our unknown value equals negative B plus R minus the square root of B squared minus four AC. And all of that will be divided by two A. So if I can find the values of A B and C from my quadratic equation, then I can plug it into. So for my unknown, now, for our quadratic equation, notice that A equals one because A is the coefficient of the squared term B is the coefficient of the linear term which is negative 10 and C is the, is the constant, which is 22. So since that's the case, that means our unknown value P would be equal to negative B that's negative, negative 10 plus R minus the square root of B squared, negative 10 squared minus four multiplied by A which is one multiplied by 22 which is C and all of that is going to be divided by two multiplied by A, that's two multiplied by one. So let's go ahead and simplify negative negative is positive 10, negative 10 squared is 100 negative four, multiplied by one is four, is negative four and negative four multiplied by 22 is negative 88. And we're going to put all of that or all of that is going to be divided by two multiplied by one, just two. Now, 100 minus 88 that equals 12. And we're at a little bit of a crossroad here because 12 is not a square number. So we won't have a whole number as its square root. However, this is where our square root property comes in handy because recall that the square root property says for the spirit of our product A B is equal to the square of A multiplied by the square root of B. So I can rewrite 12 as the product of two square roots, which can help me to simplify my answer. Because if I can find a square number that's in the product of 12, I can find it square root as a whole number and continue to solve. So let's think about it. What product of 12 has a square number in it? Well, how about were multiplied by three? Because four is a square number. So using the property of square roots or the square property, I can rewrite that as 10 plus or minus the square of four multiplied by the square of three, all divided by two and no, the square of four equals two. So A P rather equals 10 plus or minus two multiplied by the skirt of three and that all being divided by two. No, I need to make my pee look better. Just give me a minute. That doesn't look like A P. It kind of looks like an R, didn't it? No to I can divide both of these terms by two because 10 divided by two is five and two multiplied by the skirt of three, divided by two would leave us with a skirt of three. Therefore, our unknown value P or solution is five plus or minus the square of three. And when we look back in our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Solve each quadratic equation using the quadratic formula. See Example 7. x² - 2x - 2 = 0

Key Concepts

Quadratic Equation

Quadratic Formula

Discriminant

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