Question

Please help me

Use (x − 4)^2 − 28 = 8 for the following:

a. Explain why (x − 4)^2 − 28 = 8 has two solutions. (5 pts)

b. Solve the equation to find the solutions. Show your work. (5 pts)

Answer 1

Answer:

a) Because both sides are perfect squares b) (x-4)² – 28 = 8

(x–4)² = 36

Square root both sides

√(x–4)² = √36

x–4 = 6

x= 10

Step-by-step explanation:

(x–4)(x–4) = 36

x² – 8x+ 16 = 36

x² – 8x – 20 = 0

(x² + 2x)( –10x – 20) = 0

x(x+2) – 10(x+2) = 0

(x+2)(x–10) = 0

x = 10 or –2

x = 10

Answer 2

a.  If the power of x is 2 then the value of x will be 2.

b.  The values of the x are 6 and -2.

What is simplification?

Simplification is to make something easier to do or understand and to make something less complicated.

Given

The equation is $\rm (x- 4)^2 - 28 = 8$.

a.  If the power of x is 2 then the value of x will be 2. And in the equation the power of x is 2 then the solution for the x will be two.

b.  The equation is $\rm (x- 4)^2 - 28 = 8$.

On simplifying

Add 28 both the sides, we have

$\rm (x- 4)^2 = 36$

Taking square root both the sides, then we have

$\rm x- 4 = \pm 6$

Add 4 both the sides,

$\rm x = \pm 6+ 4\\\\x = 6 + 4, - 6 + 4\\\\x = 10 , -2$

Thus, the values of x are 6 and -2.

More about the simplification link is given below.

https://brainly.com/question/12616840