SOLUTION: solve the soultion (12x-8)exponent2=54

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Question 214781: solve the soultion
(12x-8)exponent2=54
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%2812x-8%29%5E2=54 Start with the given equation.


12x-8=%22%22%2B-sqrt%2854%29 Take the square root of both sides.


12x-8=sqrt%2854%29 or 12x-8=-sqrt%2854%29 Break up the "plus/minus" to form two equations.


12x-8=3%2Asqrt%286%29 or 12x-8=-3%2Asqrt%286%29 Simplify the square root.


12x=8%2B3%2Asqrt%286%29 or 12x=8-3%2Asqrt%286%29 Add 8 to both sides.


x=%288%2B3%2Asqrt%286%29%29%2F12 or x=%288-3%2Asqrt%286%29%29%2F12 Divide both sides by 12 to isolate 'x'.

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Answer:


So the solutions are x=%288%2B3%2Asqrt%286%29%29%2F12 or x=%288-3%2Asqrt%286%29%29%2F12 .

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(12x-8)exponent2=54
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(12x-8)^2 = 54
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144x^2 - 192x + 64 = 54
144x^2 - 192x + 10 = 0
72x^2 - 96x + 5 = 0
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use the quadratic formula:
x = [96 +- sqrt(96^2 - 4*72*5)]/144
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x = [96 +- sqrt(7776)]/144
x = [96 +- 88.182]/144
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x = [96 + 88.182]/144 or x = [96-88.182]/144
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x = 1.2790.. or x = 0.05429..
Cheers,
Stan H.