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

Question

Solve each quadratic equation using the quadratic formula. See Example 7. x² - 6x = -7

Accepted Answer

Welcome back everyone. In this problem, we want to use the quadratic formula to solve the quadratic equation. P squared minus 14 P equals negative 44. For our answer choices A is seven plus the square of five, B is five minus the square of seven C is five plus R minus the square of seven and D is seven plus R minus the square of five. Now, what do we do? Well, we want to use the quadratic formula. OK. And recall that for a quadratic equation in its general form A X squared plus BX plus C equals zero, then X equals negative B plus R minus the square root of B squared minus four AC all divided by two A. So what that tells us is that if we can tell the values of A B and C in our quadratic equation, then we'll be able to plug them into our formula and solve. But if you notice here, our quadratic equation is not in the general form. So we need to rewrite, so we need to rewrite our equation in the general form so that we can get those values of A B and C So FB squared minus P equals negative in general form, that just means setting our equation to zero. So if we add 44 to both sides, no, our right hand side becomes zero. And our left hand side is P squared minus 14 P plus 44. Now, it's in the general form, so we can go ahead and plug find the values of A B and C. Now A is the coefficient of the squared term, which in this case would be one B is the coefficient of our linear term, which in this case would be negative 14 and C is our constant, which is 44. So that means our unknown value P equals negative BS negative negative 14 plus or minus the square root of B squared, negative 14 squared plus sorry minus four multiplied by A which is one multiplied by C which is 4 to 4. And we're going to be dividing all of that by two multiplied by one. So let's simplify negative negative 14 is positive 14, negative 14, R squared is 196 negative four, multiplied by one is negative four and negative four, multiplied by 44 is negative and two multiplied by one is two, no 1 96 minus 1 76. That's 20. So we have all of that being divided by two and no 20 is not a square number. So we won't get a whole number if we find it square root. But to write it in a, in a, in a where we get a square root from it, we can use the square root property and recall that the square root property says that the square root of a product A B equals the square of a multiplied by the square of B. The reason that helps us is because if we can get a square number from the product, we can find its square root which would be a whole number. So let's think what product of 20 has a square number in it? Well, how about four multiplied by a five plus 20 is four, multiplied by a five and four is a square number. So now that tells us that I can rewrite this as plus or minus the square of four multiplied by the square of five all divided by two. And no, that means the square root of four equals two. So P equals 14 plus or minus two multiplied by the square of five all divided by two. And now we can go ahead and divide through by two because 14, divided by two is seven and two divided by two is one. So it would be sorry, two multiplied by the square of five, divided by two would just leave us with the square root of five. Therefore, P equals seven plus or minus the square root of five. And if we go back to our answer choices that would have been answer choice. D thanks a lot for watching everyone. I hope this video helped.

Solve each quadratic equation using the quadratic formula. See Example 7. x² - 6x = -7

Key Concepts

Quadratic Equation Standard Form

Quadratic Formula

Discriminant and Nature of Roots

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