How do you solve #-5x^2 - 8x + 1 = 0# using the quadratic formula?

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Answer 1 · 2015-08-06T13:12:45

#x_(1,2) = - (4 +- sqrt(21))/5#

For the general form quadratic equation

#color(blue)(ax^2 = bx + c = 0)#

the two solutions can be deterimed by using the quadratic formula

#color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a))#

In your case, you have #a=-5#, #b=-8#, and #c=1#. The two solutions will take the form

#x_(1,2) = (-(-8) +- sqrt( (-8)^2 - 4 * (-5) * 1))/(2 * (-5))#

#x_(1,2) = (8 +- sqrt(84))/(-10) = - (4 +- sqrt(21))/5#

This is equivalent to

#x_1 = color(green)(- (4 + sqrt(21))/5)# and #x_2 = color(green)(- (4 - sqrt(21))/5)#