Solve by factoring trinomials: x^2+5x=6

Question

Have to zero out the 6. Please explain all the steps. There can be 2 answers

Answer 1

x^2 +5x = 6

x^2 +5x -6 =0

(x+6)(x-1)= 0

x+6=0, x-1=0

x=1, x=-6

Answer 2

I can give this one a try, Alia.

Ok, so we want to solve by factoring the quadratic equation: x^2 + 5x = 6.

1.) First, move all terms to one side of the equation to set the equation to 0: x^2 + 5x - 6 = 0. Our new equation becomes x^2 + 5x - 6 = 0. Notice how this equation is the exact same as the equation stated in the problem, x^2 + 5x = 6; but this new equation is in a better "form" that allows us to factor, which is what we will do in the next step. I hope that makes sense.

2.) Next, factor our new equation x^2 + 5x - 6 = 0 by asking yourself this: "What two numbers add up to 5 and multiply together to get -6." If you notice, 5 is our second term and -6 is our third term in our quadratic equation x^2 + 5x - 6 = 0. The two numbers that add up to 5 and multiply together to get -6 are 6 and -1. Thus x^2 + 5x - 6 = 0 factors to (x + 6)(x - 1) = 0.

Note: A good way to check you have factored correctly is just to expand and see if you get the same quadratic equation. Here, (x + 6)(x - 1) = 0 = x^2 -1x + 6x + 6*(-1) = x^2 + 5x - 6 = 0. This is just our quadratic equation after we moved everything to one side, so we have factored correctly.

3.) Set each factor equal to 0 and solve for x: x + 6 = 0 and x - 1 = 0. This yields x = -6 and x = 1. So, the solutions to the equation x^2 + 5x = 6 are x = -6 and x = 1.

Hence, x = -6 and x = 1 are solutions to the equation x^2 + 5x = 6.

You can verify both solutions by plugging each solution in for x in the quadratic equation x^2 + 5x = 6 and seeing if you get 6. For example, for our solution x = -6, you can see that plugging in -6 for x, we get (-6)^2 + 5*(-6) = 36 - 30 = 6, which is indeed equal to 6. Note that you could also verify our solution by plugging in -6 for x in the quadratic equation x^2 + 5x - 6 = 0 and seeing if you get 0.

I will leave it up to you to verify our solution x = 1. All the best!