How do you solve #-2x ^ { 2} - 13x - 15= 0#?

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Answer 1 · 2017-05-04T22:59:21

See a solution process below:

Playing with the factors of #2# (1x2) and factors of #15# (1x15, 3x5) allows us to factor the left side of the equation as:

#(2x + 3)(-1x - 5) = 0#

We can now solve each term on the left side of the equation for #0# to solve the equation:

Solution 1)

#2x + 3 = 0#

#2x + 3 - color(red)(3) = 0 - color(red)(3)#

#2x + 0 = -3#

#2x = -3#

#(2x)/color(red)(2) = -3/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -3/2#

#x = -3/2#

Solution 2)

#-1x - 5 = 0#

#-1x - 5 + color(red)(5) = 0 + color(red)(5)#

#-1x - 0 = 5#

#-1x = 5#

#color(red)(-1) * -1x = color(red)(-1) * 5#

#1x = -5#

#x = -5#