SOLUTION: {{{ sqrt (b)-6=-2* sqrt(b) }}} solve each radical equation. Please help

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Question 712446: +sqrt+%28b%29-6=-2%2A+sqrt%28b%29+
solve each radical equation.
Please help
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Square both sides and simplify. Square again both sides and simplify again.

The situation you were given is based on having summable irrational numbers, so you can't simply bring them together as factors.

+sqrt+%28b%29-6=-2%2A+sqrt%28b%29+
b-12*sqrt(b)+36=4*b
-12%2Asqrt%28b%29=4b-36-b
12%2Asqrt%28b%29=b-4b%2B36
12%2Asqrt%28b%29=36-3b
12%2Asqrt%28b%29=3%2812-b%29
4%2Asqrt%28b%29=12-b

16%2Ab=144-24b%2Bb%5E2
highlight%28b%5E2-40b%2B144=0%29
Using general solution to quadratic formula, to avoid looking for factoring the trinomial, b=4 or b=36; but you should test to see if both of these will work in the original equation.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt+%28b%29+-+6=+-2%2A+sqrt%28b%29+
Add +2%2Asqrt%28b%29+ to each side
then add +6+ to both sides
+sqrt%28b%29+%2B+2%2Asqrt%28b%29+=+6+
+3%2Asqrt%28b%29+=+6+
+sqrt%28b%29+=+2+
Square both sides
+b+=+4+
---------
check:
+sqrt+%28b%29+-+6=+-2%2A+sqrt%28b%29+
+sqrt+%284%29+-+6=+-2%2A+sqrt%284%29+
+2+-+6+=+-2%2A2+
+-4+=+-4+
OK