SOLUTION: four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically

Algebra ->  Radicals -> SOLUTION: four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically      Log On


   

Question 308442: four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically
Found 2 solutions by stanbon, JBarnum:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
four times the square root of the quantity of 3a+4 equals a+13. I know the answers are 7 and 15 but cannot figure out how to get them algebraically
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4(sqrt(3a+4)) = a+13
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Square both sides to get:
16(3a+4) = a^2+26a+169
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48a+64 = a^2+26a+169
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a^2 - 22a + 105 = 0
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(a-15)(a-7) = 0
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a = 15 or a = 7
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Cheers,
Stan H.

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
4%28sqrt%283a%2B4%29%29=a%2B13square everything
4%5E2%28sqrt%283a%2B4%29%29%5E2=%28a%2B13%29%5E2
16%283a%2B4%29=%28a%2B13%29%28a%2B13%29distribute
48a%2B64=a%5E2%2B26a%2B169 subtract 48a and 64 from both sides
0=a%5E2-22a%2B105 -7 and -15 both multiply to get +105 and add to get -22
0=%28a-7%29%28a-15%29
highlight%287=a%29highlight%2815=a%29