Answer:
x = sqrt(33)/4 - 3/4 or x = -3/4 - sqrt(33)/4
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 + 3 x - 3 = 0
Divide both sides by 2:
x^2 + (3 x)/2 - 3/2 = 0
Add 3/2 to both sides:
x^2 + (3 x)/2 = 3/2
Add 9/16 to both sides:
x^2 + (3 x)/2 + 9/16 = 33/16
Write the left hand side as a square:
(x + 3/4)^2 = 33/16
Take the square root of both sides:
x + 3/4 = sqrt(33)/4 or x + 3/4 = -sqrt(33)/4
Subtract 3/4 from both sides:
x = sqrt(33)/4 - 3/4 or x + 3/4 = -sqrt(33)/4
Subtract 3/4 from both sides:
Answer: x = sqrt(33)/4 - 3/4 or x = -3/4 - sqrt(33)/4
