Answer:
x = 1/66 + sqrt(863/5)/66 or x = 1/66 - sqrt(863/5)/66
Explanation:
Solve for x:
330 x^2 - 6 = 10 x + 7
Subtract 10 x + 7 from both sides:
330 x^2 - 10 x - 13 = 0
Divide both sides by 330:
x^2 - x/33 - 13/330 = 0
Add 13/330 to both sides:
x^2 - x/33 = 13/330
Add 1/4356 to both sides:
x^2 - x/33 + 1/4356 = 863/21780
Write the left hand side as a square:
(x - 1/66)^2 = 863/21780
Take the square root of both sides:
x - 1/66 = sqrt(863/5)/66 or x - 1/66 = -sqrt(863/5)/66
Add 1/66 to both sides:
x = 1/66 + sqrt(863/5)/66 or x - 1/66 = -sqrt(863/5)/66
Add 1/66 to both sides:
Answer: x = 1/66 + sqrt(863/5)/66 or x = 1/66 - sqrt(863/5)/66