# Math Help - solving radical equations

directions say to find all solutions

1. (x + 4)^1\2 + 5x(x + 4)^3/2 = 0

I don't know how to get rid of the fractions when there are two of them
any help appreciated

2. Originally Posted by isundae
directions say to find all solutions

1. (x + 4)^1\2 + 5x(x + 4)^3/2 = 0

I don't know how to get rid of the fractions when there are two of them
any help appreciated
$(x+4)^{1/2} + 5x(x+4)^{3/2} = 0$

factor ...

$(x+4)^{1/2}[1 + 5x(x+4)] = 0$

$(x+4)^{1/2}(5x^2 + 20x + 1) = 0$

set each factor equal to 0 and solve ...

$x = -4$

$x = \frac{-10 \pm \sqrt{95}}{5}$

3. (x + 4)^(1/2) + 5x(x + 4)^(1+1/2) = 0, by factoring (x + 4)^(1/2).

(x + 4)^(1/2)(1 + (5x)(x + 4)) = 0,

(x + 4)^(1/2)(1 + 20x + 5x^2) = 0

THESE are the 3 roots:
x_1 = -4,
x_2 = -2 - sqrt (19/5) = -3.95
x_3 = sqrt (19/5) - 2 = -0.05

see graph,