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square root x+2 = 5- square root x-3
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√(x+2)=5-√(x-3)
place all radicals on one side of the equation
√(x+2)+√(x-3)=5
square both sides; eg,(a+b)^2=(a^2+2ab+b^2)
x+2+2√(x+2)(x-3)+x-3=25
place all radicals on one side of the equation again
2√(x+2)(x-3)=25+1-2x=26-2x
square both sides again
4(x+2)(x-3)=26^2+2*26*-2x+4x^2
4(x^2-x-6)=676-104x+4x^2
4x^2-4x-24=676+104x+4x^2
100x=700
x=7
Check:
√(x+2)=5-√(x-3)
√(7+2)=5-√(7-3)
√9=5-√4
3=5-2=3
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