Answer:
x = 3/10 + (i sqrt(71))/10 or x = 3/10 - (i sqrt(71))/10
Step-by-step explanation:
Solve for x:
5 x^2 - 3 x + 4 = 0
Divide both sides by 5:
x^2 - (3 x)/5 + 4/5 = 0
Subtract 4/5 from both sides:
x^2 - (3 x)/5 = -4/5
Add 9/100 to both sides:
x^2 - (3 x)/5 + 9/100 = -71/100
Write the left hand side as a square:
(x - 3/10)^2 = -71/100
Take the square root of both sides:
x - 3/10 = (i sqrt(71))/10 or x - 3/10 = -(i sqrt(71))/10
Add 3/10 to both sides:
x = 3/10 + (i sqrt(71))/10 or x - 3/10 = -(i sqrt(71))/10
Add 3/10 to both sides:
Answer: x = 3/10 + (i sqrt(71))/10 or x = 3/10 - (i sqrt(71))/10
