Y = - 4x2 - 24x - 29

x = sqrt (7) / 2 - 3 or x = - 3 - sqrt (7) / 2

Step-by-step 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