What are the solution(s) of #5 - 10x - 3x^2 = 0#?

1 Answer
Oct 21, 2015

Answer:

#x_(1,2) = -5/3 ∓ 2/3sqrt(10)#

Explanation:

For a general form quadratic equation

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

you can find its roots by using the quadratic formula

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

The quadratic equation you were given looks like this

#5 - 10x - 3x^2 = 0#

Rearrange it to match the general form

#-3x^2 - 10x + 5 = 0#

In your case, you have #a = -3#, #b = -10#, and #c = 5#. This means that the two roots will take the form

#x_(1,2) = (-(-10) +- sqrt((-10)^2 - 4 * (-3) * (5)))/(2 * (-3))#

#x_(1,2) = (10 +- sqrt(100 + 60))/((-6))#

#x_(1,2) = (10 +- sqrt(160))/((-6)) = -5/3 ∓ 2/3sqrt(10)#

The two solutions will thus be

#x_1 = -5/3 - 2/3sqrt(10)" "# and #" "x_2 = -5/3 + 2/3sqrt(10)#