10 completing the square 2. solve the equation by completing the square. show your work. x2 – 30x = –125 step 1: add to both sides of the equation. (2 points) step 2: factor the left side of the equation. show your work. (2 points) hint: it is a perfect square trinomial. step 3: take the square root of both sides of the equation from step 2. (1 point) step 4: simplify the radical and solve for x. show your work. (1 point)

Completing the Square

2. Solve the equation by completing the square. Show your work.

x^2 – 30x = –125

Step 1: Add to both sides of the equation. (2 points)

Add 225 both sides of the equation

x^2 – 30x + 225 = –125 + 225

x^2 - 30x + 225 = 100

Step 2: Factor the left side of the equation. Show your work. (2 points)

Hint: It is a perfect square trinomial.

x^2 - 30x + 225 = 100

Factor the left side of the equation:

(x - 15)^2 = 100

Step 3: Take the square root of both sides of the equation from Step 2. (1 point)

√(x - 15)^2 = √100

Step 4: Simplify the radical and solve for x. Show your work. (1 point)

x - 15 = + - 10

x - 15 = 10

x = 25

x - 15 = -10

x = 5

Solutions x = 25, 5

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option