How do you solve #10x ^ { 2} - x - 2 = 0#?

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Answer 1 · 2017-10-15T12:13:34

See a solution process below:

First, factor the left side of the equation as:

#(5x + 2)(2x - 1) = 0#

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

Solution 1:

#5x + 2 = 0#

#5x + 2 - color(red)(2) = 0 - color(red)(2)#

#5x + 0 = -2#

#5x = -2#

#(5x)/color(red)(5) = -2/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -2/5#

#x = -2/5#

Solution 2:

#2x - 1 = 0#

#2x - 1 + color(red)(1) = 0 + color(red)(1)#

#2x - 0 = 1#

#2x = 1#

#(2x)/color(red)(2) = 1/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = 1/2#

#x = 1/2#

The solutions are:

#x = -2/5# and #x = 1/2#