Answer

\sqrt{x}+\sqrt{x+15}+2\sqrt{x^2+15x} = 15-2x

Rearrange the tems

\sqrt{x}+\sqrt{x+15}+2\sqrt{x^2+15x} +2x+15 -30 = 0

x+2\sqrt{x^2+15x} +x+15+\sqrt{x}+\sqrt{x+15}-30=0

(\sqrt{x}+\sqrt{x+15} )^2+\sqrt{x}+\sqrt{x+15}-30 = 0
(1)

Let

m = \sqrt{x}+\sqrt{x+15}
(2)

The equation (1) is transformed to

m^2+m-30=0

(m+6)(m-5)=0

Then we get

m = -6 or m + 5

Cancel the negative solution, we get

\sqrt{x}+\sqrt{x+15} = 5

\sqrt{x+15} = 5-\sqrt{x}

Square both sides

x+15 = 25+x-10\sqrt{x}

-10 = -10\sqrt{x}

x=1

Steven Zheng posted 4 hours ago

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