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Overview of the Different Methods of Solving a Quadratic Equation - Problem 1

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

The first step in solving a quadratic equation is to always bring everything to one side. What we really want is all our components to one side. For this particular problem that means we just want to subtract the 5x over. We’re typically used to dealing with our leading coefficient, our x² coefficient to be positive. So we want to bring everything over to this side, leaving us with x² minus 5 x minus 6 is equal to zero.

So now we have a number of different ways of solving this. We could factor it, we could try to use our square root property, complete the square or quadratic. In general the easiest way to tackle these things is first see if we can factor it. Looking at this, I know my factors of 6 are 6 and 1, 2 and 3 and I’m trying to get -5. This actually could work.

I know that I need a x and an x and in order to get a -5 and we can get a -6, we have to combine -6 and +1. 2 and 3 isn’t going to quite cut it because these have to be opposite signs. So we now just have two things being multiplied together to equal zero. Whenever multiplying two things together to equals zero, one or both of them has to be zero, so what we’re left with is x minus 6 is equal to zero, or x plus 1 is equal to zero. Solving these both out, what we end up with is, add 6 to the other side, x is equal to 6 or subtract one over, -1.

By isolating everything to one side and then factoring we were able to solve this quadratic equation.

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