X^2 - 6 = - 2x

Find the solution by completing the square

x = - 1±sqrt (7)

Step-by-step explanation:

x^2 - 6 = - 2x

Add 2x to each side

x^2 + 2x - 6 = - 2x+2x

x^2 + 2x - 6 = 0

Add 6 to each side

x^2 + 2x - 6+6 = 6

x^2 + 2x = 6

Take the coefficient of x

2

Divide by 2

2/2 = 1

Square it

1^2 = 1

Add this to each side

x^2+2x+1 = 6+1

(x+1) ^2 = 7

Take the square root of each side

sqrt ((x+1) ^2) = ±sqrt (7)

x+1 = ±sqrt (7)

Subtract 1 from each side

x+1-1 = - 1 ±sqrt (7)

x = - 1±sqrt (7)