Solve for x
x^2 + 6 x = -5
Add 9 to both sides:
x^2 + 6 x + 9 = 4
Write the left hand side as a square:
(x + 3)^2 = 4
Take the square root of both sides:
x + 3 = 2 or x + 3 = -2
Subtract 3 from both sides:
x = -1 or x + 3 = -2
Subtract 3 from both sides:
Answer: | x = -1 or x = -5
Solve for x:
x^2 + 14 x + 112 = 0
Subtract 112 from both sides:
x^2 + 14 x = -112
Add 49 to both sides:
x^2 + 14 x + 49 = -63
Write the left hand side as a square:
(x + 7)^2 = -63
Take the square root of both sides:
x + 7 = 3 i sqrt(7) or x + 7 = -3 i sqrt(7)
Subtract 7 from both sides:
x = 3 i sqrt(7) - 7 or x + 7 = -3 i sqrt(7)
Subtract 7 from both sides:
Answer: | x = 3 i sqrt(7) - 7 or x = -3 i sqrt(7) - 7
P.S. Neither solution agrees with your multiple choices!!.