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

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true