Answer:
Here are the solutions obtained by completing the square for each of the given equations:
1. x^2 + 8x - 5 = 0:
x^2 + 8x = 5
(x + 4)^2 - 16 = 5
(x + 4)^2 = 21
x + 4 = ±√21
x = -4 ±√21
Therefore, the solutions are x = -4 + √21 and x = -4 - √21.
2. x^2 + 12x + 4 = 0:
x^2 + 12x = -4
(x + 6)^2 - 36 = -4
(x + 6)^2 = 32
x + 6 = ±2√2
x = -6 ±2√2
Therefore, the solutions are x = -6 + 2√2 and x = -6 - 2√2.
3. x^2 + 18x + 90 = 0:
x^2 + 18x = -90
(x + 9)^2 - 81 = -90
(x + 9)^2 = 9
x + 9 = ±3
x = -9 ± 3
Therefore, the solutions are x = -6 and x = -12.
4. -2x^2 - 12x - 9 = 0:
Divide both sides by -2 to simplify the equation:
x^2 + 6x + 9/2 = 0
x^2 + 6x = -9/2
(x + 3)^2 - 9/4 = -9/2
(x + 3)^2 = 0
x + 3 = 0
x = -3
Therefore, the solution is x = -3.
5. 4x^2 + 8x - 9 = 0:
Divide both sides by 4 to simplify the equation:
x^2 + 2x - 9/4 = 0
x^2 + 2x = 9/4
(x + 1)^2 - 1/4 = 9/4
(x + 1)^2 = 10/4
x + 1 = ±√10/2
x = -1 ±√10/2
Therefore, the solutions are x = -1 + √10/2 and x = -1 - √10/2.