Answer:
x = sqrt(7)/2 - 3 or x = -3 - sqrt(7)/2
Explanation:
Solve for x over the real numbers:
-4 x^2 - 24 x - 29 = 0
Divide both sides by -4:
x^2 + 6 x + 29/4 = 0
Subtract 29/4 from both sides:
x^2 + 6 x = -29/4
Add 9 to both sides:
x^2 + 6 x + 9 = 7/4
Write the left hand side as a square:
(x + 3)^2 = 7/4
Take the square root of both sides:
x + 3 = sqrt(7)/2 or x + 3 = -sqrt(7)/2
Subtract 3 from both sides:
x = sqrt(7)/2 - 3 or x + 3 = -sqrt(7)/2
Subtract 3 from both sides:
Answer: x = sqrt(7)/2 - 3 or x = -3 - sqrt(7)/2