Question 949096

6w+(23w^1/2)-104=0
<pre>{{{highlight(6w + 23w^(1/2) - 104 = 0)}}}
Let {{{highlight(a = w^(1/2))}}}  
Then {{{highlight(6w + 23w^(1/2) - 104 = 0)}}} becomes: {{{6a^2 + 23a - 104 = 0}}}
{{{6a^2 + 39a - 16a - 104 = 0}}}
3a(2a + 13) – 8(2a + 13) = 0
(3a – 8)(2a + 13) = 0
3a – 8 = 0                   OR                  2a + 13 = 0
{{{a = 8/3}}}                        OR                  {{{a = - 13/2}}}            

{{{highlight(8/3 = w^(1/2))}}} ---------- Substituting {{{8/3}}} for a
{{{highlight((8/3)^2 = w^((1/2) * 2))}}} ---- Squaring both sides
{{{highlight_green(64/9 = w)}}}

{{{- 13/2 = w^(1/2)}}} ---------- Substituting {{{- 13/2}}} for a
No expression raised to a power results in a negative expression (< 0), so {{{w = 169/4}}} is an EXTRANEOUS solution.
Therefore, only solution is: {{{highlight_green(w = 64/9)}}}