SOLUTION: Please help me solve this equation: I cant get a single value for x is it even possible? {{{sqrt( x + sqrt(x))= sqrt(30)}}}

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Question 739215: Please help me solve this equation: I cant get a single value for x is it even possible? sqrt%28+x+%2B+sqrt%28x%29%29=+sqrt%2830%29
Found 2 solutions by richwmiller, MathLover1:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt( x + sqrt(x))= sqrt(30)
x + sqrt(x)= 30
25+5=30
x=25

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28+x+%2B+sqrt%28x%29%29=+sqrt%2830%29.....raise both sides to power of 2

%28sqrt%28+x+%2B+sqrt%28x%29%29%29%5E2=+%28sqrt%2830%29%29%5E2

+x+%2B+sqrt%28x%29=+30

+sqrt%28x%29=+30-x


+sqrt%28x%29=+30-x ...raise both sides to power of 2 again

+%28sqrt%28x%29%29%5E2=+%2830-x%29%5E2

+x=+30%5E2-60x%2Bx%5E2

+0=+900-60x-x%2Bx%5E2
+x%5E2-61x%2B900=0....use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-61%29+%2B-+sqrt%28+%28-61%29%5E2-4%2A1%2A900+%29%29%2F%282%2A1%29+

x+=+%2861+%2B-+sqrt%28+3721-3600+%29%29%2F2+
x+=+%2861+%2B-+sqrt%28+121+%29%29%2F2+
x+=+%2861+%2B-+11+%29%2F2+

solutions:
x+=+%2861+%2B+11+%29%2F2+
x+=+72%2F2+
x+=+36+.......since we need +x+%2B+sqrt%28x%29=+30, this is not solution for your problem because 36%3E30

x+=+%2861+-+11+%29%2F2+
x+=+50%2F2+
x+=+25+......here 25%3C30 and this is your solution
so, sqrt%28+x+%2B+sqrt%28x%29%29=+sqrt%2830%29 is true for x+=+25+