Fifth Dimension Vector Maybe?

Algebra Level 4

a1+2b4+3c9+4d16+5e25=a+b+c+d+e2\sqrt{a-1} + 2\sqrt{b-4} +3\sqrt{c-9} +4\sqrt{d-16} +5\sqrt{e-25} =\frac{a+b+c+d+e}{2}

Five real numbers a,b,c,d,ea,b,c,d,e satisfy the equation above. Find a+b+c+d+ea+b+c+d+e .

Image Credit: Wikimedia Linearly Dependent Vectors by Super Rad!
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