What number would you add to both sides of x2 – 20x = 5 to complete the square?

answer:

we have to add 100 to both sides to complete the square.

step-by-step explanation:

the given equation is

on comparing with

a = 1

b = -20

c=5

now, in order to solve it by completing square method, we add both sides by

so we have to add 100 to both sides of the equation

let us check by adding 100 to both sides

we can rewrite the left hand side of the equation as

thus, the left hand side of the equation is a perfect square.

hence, we have to add 100 to both sides to complete the square.

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