![]() Her teacher might want to consider drawing the blinds. D'oh! The student should have first subtracted 7 from each side, then solved the equation x 2 + 3 x – 13 = 0. The original equation didn't have zero on one side. Sample ProblemĪ student, the same hopeless daydreamer who aspires to one day be a member of the National Audubon Society, was asked to use the quadratic formula to solve the equation x 2 + 3 x – 6 = 7. By the way, if you ever go overseas, make sure you pack your European quadratic plug adapter. Because we must have zero on one side of the equation, you can't go quadratic equation-happy and start plugging everything under the sun into it. The two solutions to the equation are:īe Careful: In order to use the quadratic formula, you need an equation of the form ax 2 + bx + c = 0. Since 53 is a prime number, we can't simplify any more. ![]() The coefficient on x 2 is 1, the coefficient on x is 5, and the constant term is -7, so we have:Īll we do is plug these numbers into the quadratic formula,, and we'll have our solution in no time: Try to make it feel at home, won't you? Sample Problem It's unlikely that you'll be asked in school to explain where the quadratic formula comes from, but it's reassuring to know that, like babies, it does come from somewhere. Yes, we went with "wax lips."Īs complicated as it is to arrive at and understand the quadratic formula, it's one of those things that's best to memorize and use. It's like one of those factory machines where you throw in various ingredients, and then out comes a gloriously wonderful Oreo, or Twinkie, or wax lips. When given a quadratic equation, we figure out which numbers correspond to a, b, and c, then plug them into the quadratic formula to find our answers. The quadratic formula is another way we can find solutions to quadratic equations. Okay, maybe it hasn't achieved that kind of fame, but it is well-known. It used to have its own talk show, and it was voted one of People's Sexiest Formulas Alive in 300 BCE. We call this gnarly equation the quadratic formula. These solutions are usually written together as: Ready for the second solution? Comin' atcha: Now, we need to solve these two equations: We summon our radical powers and take the square root of both sides. Since we have the square of a first-degree polynomial on the left and an admittedly messy number on the right, we know where to go from here. Now, writing the left-hand side of the equation as a square and the right-hand side of the equation in its new form, we need to solve the equation: It's a good feeling to look at such an ugly conglomeration of numbers, variables, fractions, and parentheses and know that you can make some sense out of it, eh? Not that you want to print it out and hang it on your bedroom wall, but still. ![]() Since, we can add the numbers on the right-hand side of the equation: The left-hand side of the equation can now be written as a square: ![]() It's not as nice-looking as what we've had in the past, but we'll go with it. Next we take (the coefficient on x), divide by 2, and square to find. Then we subtract from both sides to get it out of the way. We have a sneaking suspicion that b is 17, but that's only based on a dream we had last night, so we should probably do the math to be on the safe side.įirst, we divide both sides by a, since we don't want a coefficient on x 2 gumming up the works. We do know that a can't be 0, or we wouldn't have a quadratic equation. ![]() Here we know a, b, and c are numbers, but we don't know what any of them are. Solve the quadratic equation ax 2 + bx + c = 0 by completing the square. ![]()
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