Answer:
x = 1/14 i sqrt(3) a + (5 a)/14 or x = -1/14 i sqrt(3) a + (5 a)/14
Explanation:
Solve for x:
-a^2 + 5 a x - 7 x^2 = 0
Divide both sides by -7:
a^2/7 - (5 a x)/7 + x^2 = 0
Subtract a^2/7 from both sides:
x^2 - (5 a x)/7 = -a^2/7
Add (25 a^2)/196 to both sides:
(25 a^2)/196 - (5 a x)/7 + x^2 = -(3 a^2)/196
Write the both sides as a square:
(x - (5 a)/14)^2 = -(3 a^2)/196
Take the square root of both sides:
x - (5 a)/14 = 1/14 i sqrt(3) a or x - (5 a)/14 = -1/14 i sqrt(3) a
Add (5 a)/14 to both sides:
x = 1/14 i sqrt(3) a + (5 a)/14 or x - (5 a)/14 = -1/14 i sqrt(3) a
Add (5 a)/14 to both sides:
Answer: x = 1/14 i sqrt(3) a + (5 a)/14 or x = -1/14 i sqrt(3) a + (5 a)/14