Answer:
x = sqrt(29)/2 - 3/2 or x = -3/2 - sqrt(29)/2
Step-by-step explanation by completing the square:
Solve for x over the real numbers:
x^2 + 3 x - 5 = 0
Add 5 to both sides:
x^2 + 3 x = 5
Add 9/4 to both sides:
x^2 + 3 x + 9/4 = 29/4
Write the left hand side as a square:
(x + 3/2)^2 = 29/4
Take the square root of both sides:
x + 3/2 = sqrt(29)/2 or x + 3/2 = -sqrt(29)/2
Subtract 3/2 from both sides:
x = sqrt(29)/2 - 3/2 or x + 3/2 = -sqrt(29)/2
Subtract 3/2 from both sides:
Answer: x = sqrt(29)/2 - 3/2 or x = -3/2 - sqrt(29)/2
