Solve each equation using the quadratic formula. See Examples 5 a...

Question

Solve each equation using the quadratic formula. See Examples 5 and 6. -4x^2 = -12x + 11

Accepted Answer

Hello, everyone. We're going to use the quadratic formula to find the value of X in the equation four X squared minus 32 X plus 101 equals zero. I recall that in the quadratic formula, I want my equation to be set up as A X squared plus BX plus C equals zero. And this equation is set up that way already. So one less step we need to do, I do want to identify my a B&C. So a is four B is negative 32 And C is 101. Now that I have those, I'm gonna write out what the full quadratic formula is. So I can make sure I'm plugging it in right. So X squared equals negative B plus or minus the square root of B squared minus four times A C over two A. Now that I have all of that written out, I'm going to start plugging in my values. So X equals negative B or the opposite of B so positive 32 plus or minus the square root of negative 32 squared minus four times A, which happens to also be four times C which is and all of that's going to be over to a so two times four, Multiplying this out 32 plus or minus is still on the outside. And then square root negative 32 squared is 1024 -4 times four times 101 gives me - Over two times 4 which is eight, subtracting the numbers that I have under the radical, I still have X equals 32 plus or minus the square root of now negative over eight. So I know I need to reduce that radical. So I'm gonna bring it over to the side and do that. So the square root of negative 592 I recall that if I have a negative under a radical, I want to factor out the square to negative one And then thinking about what else I want to have a breakdown in here. I want to factor out a perfect square. In this case, 16 works because 16 times will give us the 592 square root of negative one is I square to 16 is four and we're gonna leave the square to 37 as the square to 37. So writing this nicer, I have four, I times the square to 37. I'm gonna plug that back into my quadratic formula and work on simplifying. So I get X equals 32 plus or minus four, I times the square to 37 over eight. Looking at this, I recognize each term can be reduced by four. So doing that, I get eight plus or minus I times the square to 37 over to because this has an imaginary number component, I'm gonna break this down into two separate terms. So we know that X is gonna equal 8/2 plus or minus I radical 37/2. The reason I do that is because 8/2 can be reduced to four. So I can get four plus or minus I radical 37/2. And that's my solution that X equals four plus or minus I times the square to 37/2, which is answer choice B have a nice day.

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Solve each equation using the quadratic formula. See Examples 5 and 6. -4x^2 = -12x + 11

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