SOLUTION: {{{ sqrt( x+7 )+sqrt ( 3x-2 ) =5 }}}

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Question 950012: +sqrt%28+x%2B7+%29%2Bsqrt+%28+3x-2+%29+=5+
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28+x%2B7+%29%2Bsqrt+%28+3x-2+%29+=5+
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+sqrt%28x%2B7%29+=+5+-+sqrt%283x-2%29
Square both sides
x%2B7+=+25+-+10sqrt%283x-2%29+%2B+3x-2
Collect terms and isolate the radical.
10sqrt%283x-2%29+=+2x+%2B+16
Reduce (optional)
5%2Asqrt%283x-2%29+=+x+%2B+8
Square again
25%2A%283x-2%29+=+x%5E2+%2B+16x+%2B+64
75x-50+=+x%5E2+%2B+16x+%2B+64
x%5E2+-+59x+%2B+114+=+0
(x-2)*(x-57) = 0
x = 2, x = 57
====================
x = 2 is clear.
For x = 57:
sqrt%28x%2B7%29%2B+sqrt%283x-2%29+=5
sqrt%2864%29%2B+sqrt%28169%29+=5
-8 + 13 = 5

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%28+x%2B7+%29%2Bsqrt+%28+3x-2+%29+=5+...square both sides
+%28sqrt%28+x%2B7+%29%2Bsqrt+%28+3x-2+%29%29%5E2+=5%5E2+


++x%2B7+%2B2%2Asqrt%28+x%2B7%29%2Asqrt%28+3x-2+%29%2B3x-2+=25+

++4x%2B5+%2B2sqrt%28%28x%2B7%29+%283+x-2%29%29+=25+
+2sqrt%28%28x%2B7%29%283x-2%29%29+=-4x%2B25-5+
+2sqrt%28%28x%2B7%29%283x-2%29%29+=-4x%2B20+...divide by 2
+sqrt%28%28x%2B7%29%283x-2%29%29+=-2x%2B10+..square both sides
+%28sqrt%28%28x%2B7%29%283x-2%29%29%29%5E2+=%28-2x%2B10%29%5E2+
+%28x%2B7%29%283x-2%29+=%28-2x%29%5E2-4x%2A10%2B10%5E2+
+3x%5E2%2B19x-14+=4x%5E2-40x%2B100+
+0=4x%5E2-3x%5E2-40x-19x%2B100%2B14+
x%5E2-59x%2B114=0+
%28x-2%29%28x-57%29=0+
solutions:
x=2
x=57
since given right side is 5, we can use only x=2