Why is the answer to this equation 400 and not 720?

Let's take this step by srep  .... we have  .....

√x +√(x/4) = 30

√x +√(x)/2 = 30       multiply through by 2

2√x +√(x) = 60        subtract √(x)  from both sides

2√(x)  = 60 - √(x)     square both sides

4x  = 3600 - 120√(x)  + x        simplify

120√(x)  = 3600 - 3x         square both sides again

14400x = 12960000 - 21600x + 9x²      simplify again

9x² - 36000x + 12960000 = 0     divide through by 9

x² - 4000x + 1440000   = 0     factor this 

(x-400) (x - 3600) = 0    

So.....x = 400 or x = 3600

Reject 3600 since it makes the original equation untrue

So ...   x = 400 is the only solution

Hi,

welcome to the forum!

with  $${\sqrt{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right){\mathtt{\,\times\,}}{\mathtt{x}}}} = \left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\sqrt{{\mathtt{x}}}}$$ your input is equal to:

$${\sqrt{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\sqrt{{\mathtt{x}}}} = {\mathtt{30}}$$

$${\sqrt{{\mathtt{x}}}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right) = {\mathtt{30}}$$

$${\sqrt{{\mathtt{x}}}} = {\frac{{\mathtt{30}}}{{\mathtt{1.5}}}}$$

$${\sqrt{{\mathtt{x}}}} = {\mathtt{20}}$$

x = 20^2 = 400

Third line, 2√(x) + √(x) = 60, so 3√(x) = 60 etc. ?