What is the positive solution of 2x^2+x=15 ?

Question

please help me solve this problem ...

Answer 1

2x² + x = 15

Start by subtracting 15 from both sides:

2x² + x - 15 = 0

As you can now see, we have a quadratic. From here comes the factoring. 2 is a prime number, so that's the easy part:

(2x ± m)(x ± n)

 

Now to find m and n. Since we have a -15, we know that one of the signs is going to be positive and one negative because we're multiplying m and n together to make the said 15. 3 and 5 are the obvious choices as opposed to 1 and 15 simply because they're too far away to make a 1 for the coefficient on the x in the middle. So our factor is going to look one of two ways:

(2x ± 5)(x ± 3) = 0 OR (2x ± 3)(x ± 5) = 0

 

Now we need to find a way to add m and n together to total 1, remembering that the 2 is in play here (because FOIL is going to have that 2 multiply with the n-value):

2 * 3 - 5 = 1

 

So that leaves us with the following:

(2x - 5)(x + 3) = 0

Now from here, you have two equations:

2x - 5 = 0 and

x + 3 = 0

 

Solve for x in each case, and the positive one will be your answer.