Solve this equation by factorisation: 8x^2 + 2x = 15

Question

explanation and working out please

Answer 1

8x² + 2x = 15

8x² + 2x - 15 = 0

 

To factor this we need to use "factor by grouping."

First multiply the coefficient of the square term, 8, by

the constant, -15.   8(-15) = -120.

Now look for factors of -120 that will add to the coefficient

of the x term, 2.  That is 12(-10).  Replace 2x with 12x - 10x

 

8x² -10x + 12x - 15 = 0

Now group the first two terms and last two terms and factor them.

(8x² - 10x) + (12x - 15) = 0

2x(4x - 5) + 3(4x - 5) = 0

Note that both sets here have the term (4x-5) so this is:

 

(2x + 3)(4x - 5) = 0

 

If this is zero then either 2x + 3 = 0

2x = -3

x = -3/2

 

OR

 

4x - 5 = 0

4x = 5

x = 5/4 or 1 1/4

 

Answer:  x = -3/2, 1 1/4

 

Questions?

 

Answer 2

8x² + 2x = 15

8x² + 2x - 15 = 0

(2x + 3)(x - 5) = 0

 

Can you solve and answer?