Solve 6x² +11x -35 =0

Step-by-step explanation: If you're asked to solve a quadratic equation by the method of your choice, you should always check to see if the quadratic factors before you try any other method.

In this case, we have a trinomial that

factors as the product of two binomials.

In the first position for each binomial, we will use

our factors of 6x² which are either 6x · x or 3x · 2x.

It's a good idea to try less extreme extreme factors.

That means choose factors a little closer together.

So 3x and 2x would be first on our list.

We do the same for the factors of -35.

Since our constant term is negative, it will factor

as the product of a positive times a negative.

So the factors of -35 are +7 · -5, -5 · +7, -7 · +5, +5 · -7.

Remember to reverse the order of the

factors is your lead coefficient is not 1.

The factors that work in this case are -5 and +7.

So we have (3x - 5)(2x + 7).

To check, take the product of the outer terms and inner terms.

So we have -21x + 10x which is our middle term.

Now set it equal to 0.

So we have (3x - 5)(2x + 7) = 0.

Now use the zero product property.

So either 3x - 5 = 0 or 2x + 7 = 0.

Solving each equation from here, we have x = 5/3 or x = -7/2.