SOLUTION: solve for x {{{3 sqrt(5x-6) + 2 sqrt(7 - x)= 13

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Question 906478: solve for x
solve+for+x%0D%0A%0D%0A3 sqrt(5x-6) + 2 sqrt(7 - x)= 13
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
3sqrt%285x-6%29=+13-2sqrt%287-x%29
9%285x-6%29=169-52sqrt%287-x%29%2B4%287-x%29
45x-54=169-52sqrt%287-x%29%2B28-4x
45x-54=-4x%2B197-52sqrt%287-x%29
49x-251=-52sqrt%287-x%29
2401x%5E2-24598x%2B63001=2704%287-x%29
2401x%5E2-24598x%2B63001=18928-2704x
2401x%5E2-21894x%2B44073=0
%28x-3%29%282401x-14691%29=0
Two solutions:
x-3=0
x=3
and
2401x-14691=0
2401x=14691
x=14691%2F2401
Verify both solutions.
3%2Asqrt%285%283%29-6%29%2B2sqrt%287-3%29=13
3%2Asqrt%289%29%2B2sqrt%284%29=13
3%2A3%2B2%2A2=13
9%2B4=13
13=13
Good solution.
3%2Asqrt%2873455%2F2401-6%29%2B2%2Asqrt%287-14691%2F2401%29=13
3%2Asqrt%2859049%2F2401%29%2B2%2Asqrt%282116%2F2401%29=13
3%2A%28243%2F49%29%2B2%2A%2846%2F49%29=13
%28729%2F49%29%2B%2892%2F49%29=13
821%2F49=13
16%2637%2F49=13
False, this is not a solution.
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highlight%28x=3%29