How do you factor and solve #3x^2+ 2x = 8#?

1 Answer
Apr 29, 2017

Answer:

See a solution process below:

Explanation:

First, subtract #color(red)(8)# from each side of the equation to put in standard quadratic form:

#3x^2 + 2x - color(red)(8) = 8 - color(red)(8)#

#3x^2 + 2x - 8 = 0#

Next, playing with factors of 3 (1 x 3 and 3 x 1) and factors of 8 (1 x 8, 2 x 4, 4 x 2 and 8 x 1) we can factor this as:

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

Now, solve each term for #0#:

Solution 1)

#3x - 4 = 0#

#3x - 4 + color(red)(4) = 0 + color(red)(4)#

#3x - 0 = 4#

#3x = 4#

#(3x)/color(red)(3) = 4/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 4/3#

#x = 4/3#

Solution 2)

#x + 2 = 0#

#x + 2 - color(red)(2) = 0 - color(red)(2)#

#x + 0 = -2#

#x = -2#

The solution is: #x = 4/3# and #x = -2#