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Bradyn Braun
Mathematics
22 December, 09:31
Solve 3/3x + 1/x+4 = 10/7x solve for x
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Marlon
22 December, 09:51
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x = 14/3 + sqrt (217) / 3 or x = 14/3 - sqrt (217) / 3
Step-by-step explanation:
Solve for x:
x + 4 + 1/x = (10 x) / 7
Bring x + 4 + 1/x together using the common denominator x:
(x^2 + 4 x + 1) / x = (10 x) / 7
Cross multiply:
7 (x^2 + 4 x + 1) = 10 x^2
Expand out terms of the left hand side:
7 x^2 + 28 x + 7 = 10 x^2
Subtract 10 x^2 from both sides:
-3 x^2 + 28 x + 7 = 0
Divide both sides by - 3:
x^2 - (28 x) / 3 - 7/3 = 0
Add 7/3 to both sides:
x^2 - (28 x) / 3 = 7/3
Add 196/9 to both sides:
x^2 - (28 x) / 3 + 196/9 = 217/9
Write the left hand side as a square:
(x - 14/3) ^2 = 217/9
Take the square root of both sides:
x - 14/3 = sqrt (217) / 3 or x - 14/3 = - sqrt (217) / 3
Add 14/3 to both sides:
x = 14/3 + sqrt (217) / 3 or x - 14/3 = - sqrt (217) / 3
Add 14/3 to both sides:
Answer: x = 14/3 + sqrt (217) / 3 or x = 14/3 - sqrt (217) / 3
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