Solve for x:
2 x^2 - 3 x + 2 = 0
Divide both sides by 2:
x^2 - (3 x)/2 + 1 = 0
Subtract 1 from both sides:
x^2 - (3 x)/2 = -1
Add 9/16 to both sides:
x^2 - (3 x)/2 + 9/16 = -7/16
Write the left hand side as a square:
(x - 3/4)^2 = -7/16
Take the square root of both sides:
x - 3/4 = (i sqrt(7))/4 or x - 3/4 = 1/4 (-i) sqrt(7)
Add 3/4 to both sides:
x = 3/4 + (i sqrt(7))/4 or x - 3/4 = 1/4 (-i) sqrt(7)
Add 3/4 to both sides:
x = 3/4 + (i sqrt(7))/4 or x= 3/4 - (i sqrt(7))/4
Solve for x:
x^2 - 4 x - 5 = 0
The left hand side factors into a product with two terms:
(x - 5) (x + 1) = 0
Split into two equations:
x - 5 = 0 or x + 1 = 0
Add 5 to both sides:
x = 5 or x + 1 = 0
Subtract 1 from both sides:
x = 5 or x = -1
