X^2 + Căn(X+5)=5

Step by step solution :

Step 1 :

Isolate a square root on the left hand side :

Radical already isolated √x-5=5-√x

Step 2 :

Eliminate the radical on the left hand side :

Raise both sides to the second power(√x-5)2=(5-√x)2After squaring x-5=x+25-10√x

Step 3 :

Get remaining radical by itself :

Current equation x-5=x+25-10√xIsolate radical on the left hand side10√x=-x+5+x+25 Tidy up 10√x=30

Step 4 :

Eliminate the radical on the left hand side :

Raise both sides to the second power(10√x)2=(30)2After squaring 100x=900

Step 5 :

Solve the linear equation :

Rearranged equation100x-900=0Add 900 to both sides 100x=900Divide both sides by 100 A possible solution is : x=9

Step 6 :

Check that the solution is correct :

Original equation, root isolated, after tidy up√x-5=5-√xPlug in 9 for x√(9)-5=5-√(9)Simplify√4=2Solution checks !!Solution is: x=9

One solution was found :

x=9


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