Question

Find the solutions to the equation below.

Check all the apply.

16x^2 - 64 = 0

A. x = 4

B. x = 2

C. x = -64

D. x = -2

E. x = -4

F. x = -8

Answer 1

B.x=2

Explanation:

`16x ^(2) - 64 = 0`

`16x ^(2) = 64`

`4 ^(2) {x}^(2) = {4}^(3)`

`{x}^(2) = (4 ^(3) )/(4 ^(2) )`

`x^(2) = 4`

`\sqrt{x ^(2) } = √(4)`

`x = 2`

Answer 2

x = 2

x = - 2

Explanation:

⇒ 1: Common Factor

• 16x² - 64 = 0
• 16(x² - 4) = 0

⇒ 2: Use the sum-product pattern

• 16 (x² - 4) = 0
• 16 (x² + 2x - 2x - 4) = 0

⇒ 3: Common factor from the two pairs

• 16((x² + 2x) + (-2x - 4) = 0
• 16(x(x+2)-2(x+2))=0

I dont feel like adding more details.

- rewrite in factored form

16(x(x+2)-2(x+2))=0

16(x-2)(x+2)=0

- create seperate equations

16(x-2)(x+2)=0

x-2=0

x+2=0

- solve

*rearrange and isolate the variable to find each solution

x = -2

x = 2