How do you solve #7n ^ { 2} + n - 8= 0#?

Question

604 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-27T02:16:32

See a solution process below:

First, factor the quadratic on the left side of the equation as:

#(7n + 8)(n - 1) = 0#

Now, solve each term on the left side of the equation for #0#:

Solution 1)

#7n + 8 = 0#

#7n + 8 - color(red)(8) = 0 - color(red)(8)#

#7n + 0 = -8#

#7n = -8#

#(7n)/color(red)(7) = -8/color(red)(7)#

#(color(red)(cancel(color(black)(7)))n)/cancel(color(red)(7)) = -8/7#

#n = -8/7#

Solution 2)

#n - 1 = 0#

#n - 1 + color(red)(1) = 0 + color(red)(1)#

#n - 0 = 1#

#n = 1#

The solution is: #n = -8/7# and #n = 1#