Question

0=x^2-8x-32 solve by completing the square

Answer 1

x = 4 ± 4
`√(3)`

Explanation:

x² - 8x - 32 = 0 ( add 32 to both sides )

x² - 8x = 32

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 32 + 16

(x - 4)² = 48 ( take square root of both sides )

x - 4 = ±
`√(48)` = ± 4
`√(3)` ( add 4 to both sides )

x = 4 ± 4
`√(3)`

Answer 2

x = 4.65 or x = -0.65 (to 2 d.p)

Explanation:

To complete the square, use the formula x² + bx + c = (x + b/2)² - (b/2)² + c

• In this case, x² - 8x - 32 = (x - 4)² - 16 - 32
• This simplifies to (x - 4)² - 48 = 0

To solve this:

• First, add 48 to both sides → (x - 4)² = 48
• Next, square root both sides → x - 4 = ± √48 (remember that the square root of a number always has a positive and negative value)
• Finally, add 4 to both sides → x = 4 ± √7

x has 2 solutions

x = 2 + √7 or x = 2 - √7

x = 4.65 or x = -0.65 (to 2 d.p)

Hope this helps!