Answer:
x = 1 or x = -5/2
Explanation:
Solve for x over the real numbers:
2 x^2 + 3 x - 2 = 3
Divide both sides by 2:
x^2 + (3 x)/2 - 1 = 3/2
Add 1 to both sides:
x^2 + (3 x)/2 = 5/2
Add 9/16 to both sides:
x^2 + (3 x)/2 + 9/16 = 49/16
Write the left hand side as a square:
(x + 3/4)^2 = 49/16
Take the square root of both sides:
x + 3/4 = 7/4 or x + 3/4 = -7/4
Subtract 3/4 from both sides:
x = 1 or x + 3/4 = -7/4
Subtract 3/4 from both sides:
Answer: x = 1 or x = -5/2