Answer :
Answer:
x = 4.65 or x = -0.65 (to 2 d.p)
Step-by-step 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!
Answer:
x = 4 ± 4[tex]\sqrt{3}[/tex]
Step-by-step 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 = ± [tex]\sqrt{48}[/tex] = ± 4[tex]\sqrt{3}[/tex] ( add 4 to both sides )
x = 4 ± 4[tex]\sqrt{3}[/tex]