{2x}^(2) + 2x + 6 = 0 equation with the variables​

Question

`{2x}^(2) + 2x + 6 = 0`
equation with the variables​

Answer 1

Solving Quadratic Equations by Completing the Square

Answer:

`x = (i√(11) -1)/(2)\\` and
`x = -(i√(11) +1)/(2)\\`

Explanation:

Given:

`2x^2 +2x +6 = 0`

Solution:

`2x^2 +2x +6 = 0 \\ 2x^2 +2x = -6 \\ x^2 + x = -3 \\ x^2 +x +(1)/(4) = -3 +(1)/(4) \\ (x +(1)/(2))^2 = -(12)/(4) +(1)/(4) \\ (x +(1)/(2))^2 = -(11)/(4) \\ x +(1)/(2) = ±\sqrt{-(11)/(4)} \\ x +(1)/(2) = ±(i√(11))/(2)`

Solving for the positive square root:

`x +(1)/(2) = (i√(11))/(2) \\ x = (i√(11))/(2) -(1)/(2) \\ x = (i√(11) -1)/(2)`

Solving for the negative square root:

`x +(1)/(2) = -(i√(11))/(2) \\ x = -(i√(11))/(2) -(1)/(2) \\ x = (-i√(11) -1)/(2) \\ x = -(i√(11) +1)/(2)`