What is the square root property of:

The square root property seems to be another name for completing the square

x^2 + 5x + 6 = 0

We move the constant to the other side

x^2 + 5x = -6

We square half the linear coefficient and add that to both sides

x^2 + 5x + (5/2)^2 = -6 + 25/4

Now the left side is a perfect square,

(x + 5/2)^2 = 1/4

Here's the square root property part, we take the square root of both sides, remembering the ±

x + 5/2 = ± 1/2

x = -5/2 ± 1/2

x = -3 or x=-2

We check by plugging in these values to the original equation, and they work.

x^2 + 6x = 16

Again we add half the linear coefficient, squared, to both sides

x^2 + 6x + 3^2 = 16 + 9

(x + 3)^2 = 25

Here comes the square root property, taking the square root of both sides:

x + 3 = ±5

x = -3 ± 5

x = 2 or x = -8

Again we check by substitution, and they both work

x = 2 or x = -8

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)